Miracle-dz/UniFAR-FTUs huggingface dataset:
From dual-unitary to quantum Bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy

Deterministic classical dynamical systems have an ergodic hierarchy, from ergodic through mixing, to Bernoulli systems that are"as random as a coin-toss". Dual-unitary circuits have been recently introduced as solvable models of many-body nonintegrable quantum chaotic systems having a hierarchy of ergodic properties. We extend this to include the apex of a putative quantum ergodic hierarchy which is Bernoulli, in the sense that correlations of single and two-particle observables vanish at space-time separated points. We derive a condition based on the entangling power $e_p(U)$ of the basic two-particle unitary building block, $U$, of the circuit, that guarantees mixing, and when maximized, corresponds to Bernoulli circuits. Additionally we show, both analytically and numerically, how local-averaging over random realizations of the single-particle unitaries, $u_i$ and $v_i$ such that the building block is $U^\prime = (u_1 \otimes u_2 ) U (v_1 \otimes v_2 )$ leads to an identification of the average mixing rate as being determined predominantly by the entangling power $e_p(U)$. Finally we provide several, both analytical and numerical, ways to construct dual-unitary operators covering the entire possible range of entangling power. We construct a coupled quantum cat map which is dual-unitary for all local dimensions and a 2-unitary or perfect tensor for odd local dimensions, and can be used to build Bernoulli circuits.
Simultaneous Monte Carlo analysis of parton densities and fragmentation functions

We perform a comprehensive new Monte Carlo analysis of high-energy lepton-lepton, lepton-hadron and hadron-hadron scattering data to simultaneously determine parton distribution functions (PDFs) in the proton and parton to hadron fragmentation functions (FFs). The analysis includes all available semi-inclusive deep-inelastic scattering and single-inclusive ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data for pions, kaons and unidentified charged hadrons, which allows the flavor dependence of the fragmentation functions to be constrained. Employing a new multistep fitting strategy and more flexible parametrizations for both PDFs and FFs, we assess the impact of different datasets on sea quark densities and confirm the previously observed suppression of the strange quark distribution. The new fit, which we refer to as ``JAM20-SIDIS,'' will allow for improved studies of universality of parton correlation functions, including transverse momentum dependent (TMD) distributions, across a wide variety of process, and the matching of collinear to TMD factorization descriptions.
On the Practicality of Differential Privacy in Federated Learning by Tuning Iteration Times

In spite that Federated Learning (FL) is well known for its privacy protection when training machine learning models among distributed clients collaboratively, recent studies have pointed out that the naive FL is susceptible to gradient leakage attacks. In the meanwhile, Differential Privacy (DP) emerges as a promising countermeasure to defend against gradient leakage attacks. However, the adoption of DP by clients in FL may significantly jeopardize the model accuracy. It is still an open problem to understand the practicality of DP from a theoretic perspective. In this paper, we make the first attempt to understand the practicality of DP in FL through tuning the number of conducted iterations. Based on the FedAvg algorithm, we formally derive the convergence rate with DP noises in FL. Then, we theoretically derive: 1) the conditions for the DP based FedAvg to converge as the number of global iterations (GI) approaches infinity; 2) the method to set the number of local iterations (LI) to minimize the negative influence of DP noises. By further substituting the Laplace and Gaussian mechanisms into the derived convergence rate respectively, we show that: 3) The DP based FedAvg with the Laplace mechanism cannot converge, but the divergence rate can be effectively prohibited by setting the number of LIs with our method; 4) The learning error of the DP based FedAvg with the Gaussian mechanism can converge to a constant number finally if we use a fixed number of LIs per GI. To verify our theoretical findings, we conduct extensive experiments using two real-world datasets. The results not only validate our analysis results, but also provide useful guidelines on how to optimize model accuracy when incorporating DP into FL
Coarse-median preserving automorphisms

This paper has three main goals. First, we study fixed subgroups of automorphisms of right-angled Artin and Coxeter groups. If $\varphi$ is an untwisted automorphism of a RAAG, or an arbitrary automorphism of a RACG, we prove that ${\rm Fix}~\varphi$ is finitely generated and undistorted. Up to replacing $\varphi$ with a power, we show that ${\rm Fix}~\varphi$ is quasi-convex with respect to the standard word metric. This implies that ${\rm Fix}~\varphi$ is separable and a special group in the sense of Haglund-Wise. By contrast, there exist"twisted"automorphisms of RAAGs for which ${\rm Fix}~\varphi$ is undistorted but not of type $F$ (hence not special), of type $F$ but distorted, or even infinitely generated. Secondly, we introduce the notion of"coarse-median preserving"automorphism of a coarse median group, which plays a key role in the above results. We show that automorphisms of RAAGs are coarse-median preserving if and only if they are untwisted. On the other hand, all automorphisms of Gromov-hyperbolic groups and right-angled Coxeter groups are coarse-median preserving. These facts also yield new or more elementary proofs of Nielsen realisation for RAAGs and RACGs. Finally, we show that, for every special group $G$ (in the sense of Haglund-Wise), every infinite-order, coarse-median preserving outer automorphism of $G$ can be realised as a homothety of a finite-rank median space $X$ equipped with a"moderate"isometric $G$-action. This generalises the classical result, due to Paulin, that every infinite-order outer automorphism of a hyperbolic group $H$ projectively stabilises a small $H$-tree.
Cold ion beam in a storage ring as a platform for large-scale quantum computers and simulators: Challenges and directions for research and development

The purpose of this paper is to evaluate the possibility of constructing a large-scale storage-ring-type iontrap system capable of storing, cooling, and controlling a large number of ions as a platform for scalable quantum computing (QC) and quantum simulations (QS). In such a trap, the ions form a crystalline beam moving along a circular path with a constant velocity determined by the frequency and intensity of the cooling lasers. In this paper we consider a large leap forward in terms of the number of qubits, from fewer than 100 available in state-of-the-art linear ion-trap devices today to an order of 105 crystallized ions in the storage-ring setup. This new trap design unifies two different concepts: the storage rings of charged particles and the linear ion traps used for QC and mass spectrometry. In this paper we use the language of particle accelerators to discuss the ion state and dynamics. We outline the differences between the above concepts, analyze challenges of the large ring with a revolving beam of ions, and propose goals for the research and development required to enable future quantum computers with 1000 times more qubits than available today. The challenge of creating such a large-scale quantum system while maintaining the necessary coherence of the qubits and the high fidelity of quantum logic operations is significant. Performing analog quantum simulations may be an achievable initial goal for such a device. Quantum simulations of complex quantum systems will move forward both the fundamental science and the applied research. Nuclear and particle physics, many-body quantum systems, lattice gauge theories, and nuclear structure calculations are just a few examples in which a large-scale quantum simulation system would be a very powerful tool to move forward our understanding of nature.
Coherent scattering of an optically modulated electron beam by atoms

Recent technological advances allowed the coherent optical manipulation of high-energy electron wavepackets with attosecond precision. Here we theoretically investigate the collision of optically-modulated pulsed electron beams with atomic targets and reveal a quantum interference associated with different momentum components of the incident broadband electron pulse, which coherently modulates both the elastic and inelastic scattering cross sections. We show that the quantum interference has a high spatial sensitivity at the level of Angstroms, offering potential applications in high-resolution ultrafast electron microscopy. Our findings are rationalized by a simple model.
Deposition of Particles by a Confined Impinging Jet onto a Flat Surface at Re = 10 4

An axisymmetric turbulent air jet flow (with vertical and downward orientation) laden with fluorescent solid particles was impinged normally onto a flat surface. The particle deposition efficiency and distribution on the flat surface were measured experimentally using fluorometry and imaging techniques. The fluorescent particles (5.0 μm diameter) were dispersed by a nebulizer and injected in a stream of compressed air, resulting in a steady flow (Q = 111 L/min). A round nozzle was used to generate a jet characterized by a Reynolds number of Re = 10 4 , based on the nozzle diameter (D = 15.0 mm) and nozzle exit velocity (u = 10.5 m/s). Three dimensionless distances from the nozzle's exit to the impaction surface, L/D = 2, 4, and 6, were investigated. It was observed that although having similar total deposition efficiencies (16.5–17.8%), shorter nozzle to surface distances (L/D = 2 and 4) show a more pronounced ring-like radial deposition pattern around the stagnation point. These shorter distances also exhibit significantly lower particle deposition near the stagnation point when compared to the longer distance (L/D = 6). Indeed, in moving through L/D = 2, 4, and 6, peak deposition density values of 254, 347, and 685 particles/mm 2 shift through radii of 2.1 D, 0.8 D, and 0.1 D, respectively. In addition to the experiments, numerical simulation was also performed, which showed that the particle deposition was dominated by a turbulent dispersion mechanism for L/D = 2, with inertial impaction becoming more important for the L/D = 4 and 6 cases.
CAnet: Uplink-Aided Downlink Channel Acquisition in FDD Massive MIMO Using Deep Learning

In frequency-division duplexing systems, the downlink channel state information (CSI) acquisition scheme leads to high training and feedback overhead. In this work, we propose an uplink-aided downlink channel acquisition framework using deep learning to reduce such overhead. We consider the entire downlink CSI acquisition process, including the downlink pilot design, channel estimation, and feedback. First, we propose an adaptive pilot design module by exploiting the correlation in magnitude among bidirectional channels in the angular domain to improve channel estimation. Second, to avoid the bit allocation problem during the feedback module, we concatenate the complex channel and embed the uplink channel magnitude to the channel reconstruction at the base station. Finally, we combine the two modules and compare two popular uplink-aided downlink channel acquisition frameworks. One framework estimates and subsequently feeds back the channel at the user equipment. In the other framework, the user equipment directly feeds back the received pilot signals to the base station. Results reveal that with the help of the uplink channel, directly feeding back pilot signals can save approximately 20% of feedback bits. This work thus provides a guideline for future research.
Categories of Nets

We present a unified framework for Petri nets and various variants, such as pre-nets and Kock’s whole-grain Petri nets. Our framework is based on a less well-studied notion that we call Σ-nets, which allow fine-grained control over whether each transition behaves according to the collective or individual token philosophy. We describe three forms of execution semantics in which pre-nets generate strict monoidal categories, Σ-nets (including whole-grain Petri nets) generate symmetric strict monoidal categories, and Petri nets generate commutative monoidal categories, all by left adjoint functors. We also construct adjunctions relating these categories of nets to each other, in particular showing that all kinds of net can be embedded in the unifying category of Σ-nets, in a way that commutes coherently with their execution semantics.
Superconducting Quantum Interference in Twisted van der Waals Heterostructures

We demonstrate the formation of both Josephson junctions and superconducting quantum interference devices (SQUIDs) using a dry transfer technique to stack and deterministically misalign mechanically exfoliated flakes of NbSe2. The current–voltage characteristics of the resulting twisted NbSe2–NbSe2 junctions are found to be sensitive to the misalignment angle of the crystallographic axes, opening up a new control parameter for optimization of the device performance, which is not available in thin-film-deposited junctions. A single lithographic process has then been implemented to shape Josephson junctions into SQUID geometries with typical loop areas of ∼25 μm2 and weak links ∼600 nm wide. At T = 3.75 K in an applied magnetic field, these devices display large stable current and voltage modulation depths of up to ΔIc ∼ 75% and ΔV ∼ 1.4 mV, respectively.
Time-resolved rheometry of drying liquids and suspensions

From paints to food products, solvent evaporation is ubiquitous and critically impacts product rheological properties. It affects Newtonian fluids by concentrating any nonvolatile components and viscoelastic materials, which harden up. In both of these cases, solvent evaporation leads to a change in the volume of the sample, which makes any rheological measurements particularly challenging with traditional shear geometries. Here, we show that the rheological properties of a sample experiencing “slow” evaporation can be monitored in a time-resolved fashion by using a zero normal force controlled protocol in a parallel-plate geometry. Solvent evaporation from the sample leads to a decrease of the normal force, which is compensated at all times by a decrease of the gap height between the plates. As a result, the sample maintains a constant contact area with the plates, despite the significant decrease of its volume. We validate the method under both oscillatory and continuous shear by accurately monitoring the viscosity of water–glycerol mixtures experiencing evaporation and a relative volume decrease as large as 70%. Moreover, we apply this protocol to drying suspensions. Specifically, we monitor a dispersion of charged silica nanoparticles undergoing a glass transition induced by evaporation. While the decrease in gap height provides a direct estimate of the increasing particle volume fraction, oscillatory and continuous shear measurements allow us to monitor the evolving viscoelastic properties of the suspension in real time. Overall, our study shows that a zero normal force protocol provides a simple approach to bulk and time-resolved rheological characterization for systems experiencing slow volume variations.
Of Non-Linearity and Commutativity in BERT

In this work we provide new insights into the transformer architecture, and in particular, its best-known variant, BERT. First, we propose a method to measure the degree of non-linearity of different elements of transformers. Next, we focus our investigation on the feed-forward networks (FFN) inside transformers, which contain two thirds of the model parameters and have so far not received much attention. We find that FFNs are an inefficient yet important architectural element and that they cannot simply be replaced by attention blocks without a degradation in performance. Moreover, we study the interactions between layers in BERT and show that, while the layers exhibit some hierarchical structure, they extract features in a fuzzy manner. Our results suggest that BERT has an inductive bias towards layer commutativity, which we find is mainly due to the skip connections. This provides a justification for the strong performance of recurrent and weight-shared transformer models.
Measuring very small concentrations in organic suspensions by coherent light scattering

The single act light scattering anisotropy is conveniently described using the Henyey-Greenstein phase function when the scattering centers dimension is comparable or bigger than the wave length. When the concentration increases, a different phase function can be used. For a certain scattering angle the calculated light scattering intensity variation with the optical depth of the target is analyzed and compared with the experimental data recorded on mud in aqueous suspension. The results suggest a very fast method for measuring very small concentration in suspensions, in the range of μg/l.
Multimodal Engagement Analysis From Facial Videos in the Classroom

Student engagement is a key component of learning and teaching, resulting in a plethora of automated methods to measure it. Whereas most of the literature explores student engagement analysis using computer-based learning often in the lab, we focus on using classroom instruction in authentic learning environments. We collected audiovisual recordings of secondary school classes over a one and a half month period, acquired continuous engagement labeling per student (N=15) in repeated sessions, and explored computer vision methods to classify engagement from facial videos. We learned deep embeddings for attentional and affective features by training Attention-Net for head pose estimation and Affect-Net for facial expression recognition using previously-collected large-scale datasets. We used these representations to train engagement classifiers on our data, in individual and multiple channel settings, considering temporal dependencies. The best performing engagement classifiers achieved student-independent AUCs of . 620 and . 720 for grades 8 and 12, respectively, with attention-based features outperforming affective features. Score-level fusion either improved the engagement classifiers or was on par with the best performing modality. We also investigated the effect of personalization and found that only 60 seconds of person-specific data, selected by margin uncertainty of the base classifier, yielded an average AUC improvement of . 084.
Implicit Unlikelihood Training: Improving Neural Text Generation with Reinforcement Learning

Likelihood training and maximization-based decoding result in dull and repetitive generated texts even when using powerful language models (Holtzman et al., 2019). Adding a loss function for regularization was shown to improve text generation output by helping avoid unwanted properties, such as contradiction or repetition (Li at al., 2020). In this work, we propose fine-tuning a language model by using policy gradient reinforcement learning, directly optimizing for better generation. We apply this approach to minimizing repetition in generated text, and show that, when combined with unlikelihood training (Welleck et al., 2020), our method further reduces repetition without impacting the language model quality. We also evaluate other methods for improving generation at training and decoding time, and compare them using various metrics aimed at control for better text generation output.
Modelling the delivery of dust from discs to ionized winds

A necessary first step for dust removal in protoplanetary disc winds is the delivery of dust from the disc to the wind. In the case of ionized winds, the disc and wind are sharply delineated by a narrow ionization front where the gas density and temperature vary by more than an order of magnitude. Using a novel method that is able to model the transport of dust across the ionization front in the presence of disc turbulence, we revisit the problem of dust delivery. Our results show that the delivery of dust to the wind is determined by the vertical gas flow through the disc induced by the mass loss, rather than turbulent diffusion (unless the turbulence is strong, i.e. α & 0.01). Using these results we provide a simple relation between the maximum size of particle that can be delivered to the wind and the local mass-loss rate per unit area from the wind. This relation is independent of the physical origin of the wind and predicts typical sizes in the 0.01 – 1μm range for EUV or X-ray driven winds. These values are a factor ∼ 10 smaller than those obtained when considering only whether the wind is able to carry away the grains.
On the Convergence of Deep Networks with Sample Quadratic Overparameterization

The remarkable ability of deep neural networks to perfectly ﬁt training data when optimized by gradient-based algorithms is yet to be fully explained theoretically. Explanations by recent theoretical works rely on the networks to be wider by orders of magnitude than the ones used in practice. In this work, we take a step towards closing the gap between theory and practice. We show that a randomly initialized deep neural network with ReLU activation converges to a global minimum in a logarithmic number of gradient-descent iterations, under a considerably milder condition on its width. Our analysis is based on a novel technique of training a network with ﬁxed activation patterns. We study the unique properties of the technique that allow an improved convergence, and can be transformed at any time to an equivalent ReLU network of a reasonable size. We derive a tight ﬁnite-width Neural Tangent Kernel (NTK) equivalence, suggesting that neural networks trained with our technique generalize well at least as good as its NTK, and it can be used to study generalization as well.
DBTagger: Multi-Task Learning for Keyword Mapping in NLIDBs Using Bi-Directional Recurrent Neural Networks

Translating Natural Language Queries (NLQs) to Structured Query Language (SQL) in interfaces deployed in relational databases is a challenging task, which has been widely studied in database community recently. Conventional rule based systems utilize series of solutions as a pipeline to deal with each step of this task, namely stop word filtering, tokenization, stemming/lemmatization, parsing, tagging, and translation. Recent works have mostly focused on the translation step overlooking the earlier steps by using adhoc solutions. In the pipeline, one of the most critical and challenging problems is keyword mapping; constructing a mapping between tokens in the query and relational database elements (tables, attributes, values, etc.). We define the keyword mapping problem as a sequence tagging problem, and propose a novel deep learning based supervised approach that utilizes POS tags of NLQs. Our proposed approach, called DBTagger (DataBase Tagger), is an end-to-end and schema independent solution, which makes it practical for various relational databases. We evaluate our approach on eight different datasets, and report new state-of-the-art accuracy results, 92.4% on the average. Our results also indicate that DBTagger is faster than its counterparts up to 10000 times and scalable for bigger databases.