Miracle-dz/UniFAR-FTUs huggingface dataset:
Strong ill-posedness for fractional Hartree and cubic NLS Equations

We consider fractional Hartree and cubic nonlinear Schr\"odinger equations on Euclidean space $\mathbb R^d$ and on torus $\mathbb T^d$. We establish norm inflation (a stronger phenomena than standard ill-posedness) at every initial data in Fourier amalgam spaces with negative regularity. In particular, these spaces include Fourier-Lebesgue, modulation and Sobolev spaces. We further show that this can be even worse by exhibiting norm inflation with an infinite loss of regularity. To establish these phenomena, we employ a Fourier analytic approach and introduce new resonant sets corresponding to the fractional dispersion $(-\Delta)^{\alpha/2}$. In particular, when dispersion index $\alpha$ is large enough, we obtain norm inflation {above} scaling critical regularity in some of these spaces. It turns out that our approach could treat both equations (Hartree and power-type NLS) in a unified manner. The method should also work for a broader range of nonlinear equations with Hartree-type nonlinearity.
Sub-Goal Social Force Model for Collective Pedestrian Motion Under Vehicle Influence

In mixed traffic scenarios, a certain number of pedestrians might coexist in a small area while interacting with vehicles. In this situation, every pedestrian must simultaneously react to the surrounding pedestrians and vehicles. Analytical modeling of such collective pedestrian motion can benefit intelligent transportation practices like shared space design and urban autonomous driving. This work proposed the sub-goal social force model (SG-SFM) to describe the collective pedestrian motion under vehicle influence. The proposed model introduced a new design of vehicle influence on pedestrian motion, which was smoothly combined with the influence of surrounding pedestrians using the sub-goal concept. This model aims to describe generalized pedestrian motion, i.e., it is applicable to various vehicle-pedestrian interaction patterns. The generalization was verified by both quantitative and qualitative evaluation. The quantitative evaluation was conducted to reproduce pedestrian motion in three different datasets, HBS, CITR, and DUT. It also compared two different ways of calibrating the model parameters. The qualitative evaluation examined the simulation of collective pedestrian motion in a series of fundamental vehicle-pedestrian interaction scenarios. The above evaluation results demonstrated the effectiveness of the proposed model.
Study of Nonlinear Interaction between Waves and Ocean Currents Using High-Fidelity Simulation and Machine Learning

Modeling ocean surface waves under complex ocean current conditions is of crucial importance to many naval applications. For example, traveling ships and underwater vehicles generate spatially heterogeneous currents behind them through their drag and propeller motions. The strong currents can inﬂuence the surface wave pattern in the ship wake. In this study, the nonlinear interactions between waves and complex wake currents are investigated using numerical simulations. An in-house code is developed for high-ﬁdelity simulations of a nonlinear phase-resolved ocean waveﬁeld interacting with subsurface currents. Several typical wake patterns are simulated using the present numerical method, and the inﬂuence of complex currents on the waves is analyzed quantitatively using theoretical solutions of wave–current interactions. We also present a method for solving the inverse problem of deducing the current ﬁeld based on surface-wave data using machine-learning techniques. A deep neural network is designed for processing spatial-temporal surface wave data. Detailed analyses on the distributions of regression errors and the training dataset-dependency show that the proposed neural network can effectively deduce the current ﬁeld.
Connection between Inverse Engineering and Optimal Control in Shortcuts to Adiabaticity

We consider fast high-fidelity quantum control by using a shortcut to adiabaticity (STA) technique and optimal control theory (OCT). Three specific examples, including expansion of cold atoms from the harmonic trap, atomic transport by moving harmonic trap, and spin dynamics in the presence of dissipation, are explicitly detailed. Using OCT as a qualitative guide, we demonstrate how STA protocols designed from inverse engineering method can approach with very high precision optimal solutions built about physical constraints, by a proper choice of the interpolation function and with a very reduced number of adjustable parameters.
ALMA 1.3 mm Survey of Lensed Submillimeter Galaxies Selected by Herschel: Discovery of Spatially Extended SMGs and Implications

We present an ALMA 1.3 mm (Band 6) continuum survey of lensed submillimeter galaxies (SMGs) at z = 1.0 to ∼3.2 with an angular resolution of ∼0. ″2. These galaxies were uncovered by the Herschel Lensing Survey and feature exceptionally bright far-infrared continuum emission (Speak ≳ 90 mJy) owing to their lensing magnification. We detect 29 sources in 20 fields of massive galaxy clusters with ALMA. Using both the Spitzer/IRAC (3.6/4.5 μm) and ALMA data, we have successfully modeled the surface brightness profiles of 26 sources in the rest-frame near- and far-infrared. Similar to previous studies, we find the median dust-to-stellar continuum size ratio to be small (Re,dust/Re,star = 0.38 ± 0.14) for the observed SMGs, indicating that star formation is centrally concentrated. This is, however, not the case for two spatially extended main-sequence SMGs with a low surface brightness at 1.3 mm (≲0.1 mJy arcsec−2), in which the star formation is distributed over the entire galaxy (Re,dust/Re,star > 1). As a whole, our SMG sample shows a tight anticorrelation between (Re,dust/Re,star) and far-infrared surface brightness (ΣIR) over a factor of ≃1000 in ΣIR. This indicates that SMGs with less vigorous star formation (i.e., lower ΣIR) lack central starburst and are likely to retain a broader spatial distribution of star formation over the whole galaxies (i.e., larger Re,dust/Re,star). The same trend can be reproduced with cosmological simulations as a result of central starburst and potentially subsequent “inside-out” quenching, which likely accounts for the emergence of compact quiescent galaxies at z ∼ 2.
Towards Long-term Fairness in Recommendation

As Recommender Systems (RS) influence more and more people in their daily life, the issue of fairness in recommendation is becoming more and more important. Most of the prior approaches to fairness-aware recommendation have been situated in a static or one-shot setting, where the protected groups of items are fixed, and the model provides a one-time fairness solution based on fairness-constrained optimization. This fails to consider the dynamic nature of the recommender systems, where attributes such as item popularity may change over time due to the recommendation policy and user engagement. For example, products that were once popular may become no longer popular, and vice versa. As a result, the system that aims to maintain long-term fairness on the item exposure in different popularity groups must accommodate this change in a timely fashion. Novel to this work, we explore the problem of long-term fairness in recommendation and accomplish the problem through dynamic fairness learning. We focus on the fairness of exposure of items in different groups, while the division of the groups is based on item popularity, which dynamically changes over time in the recommendation process. We tackle this problem by proposing a fairness-constrained reinforcement learning algorithm for recommendation, which models the recommendation problem as a Constrained Markov Decision Process (CMDP), so that the model can dynamically adjust its recommendation policy to make sure the fairness requirement is always satisfied when the environment changes. Experiments on several real-world datasets verify our framework's superiority in terms of recommendation performance, short-term fairness, and long-term fairness.
Density dependent diffusion models for the interaction of particle ensembles with boundaries

The transition from a microscopic model for the movement of many particles to a macroscopic continuum model for a density flow is studied. The microscopic model for the free flow is completely deterministic, described by an interaction potential that leads to a coherent motion where all particles move in the same direction with the same speed known as a flock. Interaction of the flock with boundaries, obstacles and other flocks leads to a temporary destruction of the coherent motion that macroscopically can be modeled through density dependent diffusion. The resulting macroscopic model is an advection-diffusion equation for the particle density whose diffusion coefficient is density dependent. Examples describing ⅰ) the interaction of material flow on a conveyor belt with an obstacle that redirects or restricts the material flow and ⅱ) the interaction of flocks (of fish or birds) with boundaries and ⅲ) the scattering of two flocks as they bounce off each other are discussed. In each case, the advection-diffusion equation is strictly hyperbolic before and after the interaction while the interaction phase is described by a parabolic equation. A numerical algorithm to solve the advection-diffusion equation through the transition is presented.
Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity

In deep learning, models typically reuse the same parameters for all inputs. Mixture of Experts (MoE) defies this and instead selects different parameters for each incoming example. The result is a sparsely-activated model -- with outrageous numbers of parameters -- but a constant computational cost. However, despite several notable successes of MoE, widespread adoption has been hindered by complexity, communication costs and training instability -- we address these with the Switch Transformer. We simplify the MoE routing algorithm and design intuitive improved models with reduced communication and computational costs. Our proposed training techniques help wrangle the instabilities and we show large sparse models may be trained, for the first time, with lower precision (bfloat16) formats. We design models based off T5-Base and T5-Large to obtain up to 7x increases in pre-training speed with the same computational resources. These improvements extend into multilingual settings where we measure gains over the mT5-Base version across all 101 languages. Finally, we advance the current scale of language models by pre-training up to trillion parameter models on the"Colossal Clean Crawled Corpus"and achieve a 4x speedup over the T5-XXL model.
Three-dimensional simulations of X-ray cavities inflated by radio galaxies

Vast cavities in the intergalactic medium are excavated by radio galaxies. The cavities appear as such in X-ray images because the external medium has been swept up, leaving a hot but low density bubble surrounding the radio lobes. We explore here the predicted thermal X-ray emission from a large set of high-resolution three dimensional simulations of radio galaxies driven by supersonic jets. We assume adiabatic non-relativistic hydrodynamics with injected straight and precessing jets of supersonic gas emitted from nozzles. Images of X-ray Bremsstrahlung emission tend to generate oval cavities in the soft keV bands and leading arcuate structures in hard X-rays. However, the cavity shape is sensitive to the jet-ambient density contrast, varying from concave-shaped at η = 0.1 to convex for η = 0.0001 where η is the jet/ambient density ratio. We find lateral ribs in the soft X-rays in certain cases and propose this as an explanation for those detected in the vicinity of Cygnus A. In bi-lobed or X-shaped sources and in curved or deflected jets, the strongest X-ray emission is not associated with the hotspot but with the relic lobe or deflection location. This is because the hot high-pressure and dense high-compression regions do not coincide. Directed toward the observer, the cavity becomes a deep round hole surrounded by circular ripples. With short radio-mode outbursts with a duty cycle of 10% , the intracluster medium simmers with low Mach number shocks widely dissipating the jet energy in between active jet episodes.
The Diabetic Buddy: A Diet Regulator and Tracking System for Diabetics

The prevalence of Diabetes mellitus (DM) in the Middle East is exceptionally high as compared to the rest of the world. In fact, the prevalence of diabetes in the Middle East is 17-20%, which is well above the global average of 8-9%. Research has shown that food intake has strong connections with the blood glucose levels of a patient. In this regard, there is a need to build automatic tools to monitor the blood glucose levels of diabetics and their daily food intake. This paper presents an automatic way of tracking continuous glucose and food intake of diabetics using off-the-shelf sensors and machine learning, respectively. Our system not only helps diabetics to track their daily food intake but also assists doctors to analyze the impact of the food in-take on blood glucose in real-time. For food recognition, we collected a large-scale Middle-Eastern food dataset and proposed a fusion-based framework incorporating several existing pre-trained deep models for Middle-Eastern food recognition.
Typical relaxation of perturbed quantum many-body systems

We substantially extend our relaxation theory for perturbed many-body quantum systems from ((2020) Phys. Rev. Lett. 124 120602) by establishing an analytical prediction for the time-dependent observable expectation values which depends on only two characteristic parameters of the perturbation operator: its overall strength and its range or band width. Compared to the previous theory, a significantly larger range of perturbation strengths is covered. The results are obtained within a typicality framework by solving the pertinent random matrix problem exactly for a certain class of banded perturbations and by demonstrating the (approximative) universality of these solutions, which allows us to adopt them to considerably more general classes of perturbations. We also verify the prediction by comparison with several numerical examples.
Quantum Information Theory of the Gravitational Anomaly

We show that the standard notion of entanglement is not defined for gravitationally anomalous two-dimensional theories because they do not admit a local tensor factorization of the Hilbert space into local Hilbert spaces. Qualitatively, the modular flow cannot act consistently and unitarily in a finite region, if there are different numbers of states with a given energy traveling in the two opposite directions. We make this precise by decomposing it into two observations: First, a twodimensional conformal field theory admits a consistent quantization on a space with boundary only if it is not anomalous. Second, a local tensor factorization always leads to a definition of consistent, unitary, energy-preserving boundary condition. As a corollary we establish a generalization of the Nielsen–Ninomiya theorem to all two-dimensional unitary local quantumfield theories: No continuumquantumfield theory in two dimensions can admit a lattice regulator unless its gravitational anomaly vanishes. We also show that the conclusion can be generalized to six dimensions by dimensional reduction on a four-manifold of nonvanishing signature. We advocate that these points be used to reinterpret the gravitational anomaly quantum-information-theoretically, as a fundamental obstruction to the localization of quantum information. ar X iv :2 10 1. 03 32 0v 1 [ he pth ] 9 J an 2 02 1
Learning to Automate Chart Layout Configurations Using Crowdsourced Paired Comparison

We contribute a method to automate parameter configurations for chart layouts by learning from human preferences. Existing charting tools usually determine the layout parameters using predefined heuristics, producing sub-optimal layouts. People can repeatedly adjust multiple parameters (e.g., chart size, gap) to achieve visually appealing layouts. However, this trial-and-error process is unsystematic and time-consuming, without a guarantee of improvement. To address this issue, we develop Layout Quality Quantifier (LQ2), a machine learning model that learns to score chart layouts from paired crowdsourcing data. Combined with optimization techniques, LQ2 recommends layout parameters that improve the charts’ layout quality. We apply LQ2 on bar charts and conduct user studies to evaluate its effectiveness by examining the quality of layouts it produces. Results show that LQ2 can generate more visually appealing layouts than both laypeople and baselines. This work demonstrates the feasibility and usages of quantifying human preferences and aesthetics for chart layouts.
Doubly Slice Montesinos Links

This paper compares notions of double sliceness for links. The main result is to show that a large family of 2-component Montesinos links are not strongly doubly slice despite being weakly doubly slice and having doubly slice components. Our principal obstruction to strong double slicing comes by considering branched double covers. To this end we prove a result classifying Seifert fibered spaces which admit a smooth embeddings into integer homology $S^1 \times S^3$s by maps inducing surjections on the first homology group. A number of other results and examples pertaining to doubly slice links are also given.
Determination of aflatoxin and fumonisin levels through ELISA and HPLC, on tilapia feed in Nayarit, Mexico

A survey of fungal contamination and presence of aflatoxins (AFs) and fumonisins (FBs) in 30 feed samples collected from 10 tilapia farms during three seasons in Nayarit State, located in north-western Mexico, was carried out using ELISA as screening and High-Performance Liquid Chromatography (HPLC) as confirmatory method. Mycobiota included Aspergillus flavus and Fusarium spp. AFs were detected in 63.3% of samples using ELISA, but confirmation by HPLC revealed that all samples were under the detection limit. Regarding to FBs, positive samples were detected using both methods, with 19 positive samples (60% of total) by ELISA and 14 positive samples (46.6% of total) by HPLC and levels ranging from 0.148 to 2.587 mg/kg. Correlation was observed between both methods (r = 0.516, p = 0.004) for FBs results. No sample exceeded the European maximum levels for any of the mycotoxins. Water activity of samples ranged from 0.345 to 0.655, suggesting that mycotoxin occurrence is probably related to raw material contamination.
Neue Vertreter des Er6[Si11N20]O-Strukturtyps Hochtemperatur-Synthesen und Kristallstrukturen von Ln(6+x/3)[Si(11–y)AlyN(20+x–y)]O(1–x+y) mit Ln = Nd, Er, Yb, Dy und 0 ≤ x ≤ 3, 0 ≤ y ≤ 3

Die vier Verbindungen Er6[Si11N20]O, Yb6,081[Si11N20,234]O0,757, Dy0,33Sm6[Si11N20]N und Nd7[Si8Al3N20]O der allgemeinen Formel Ln(6+x/3)[Si(11–y)AlyN(20+x–y)]O(1–x+y) (0 ≤ x ≤ 3, 0 ≤ y ≤ 3) wurden dargestellt. Die Synthese erfolgte in einem Hochfrequenzofen zwischen 1300 und 1650 °C. Die Nitridosilicate kristallisieren trigonal mit folgenden Gitterkonstanten: Er6[Si11N20]O: a = 978,8(4) pm, c = 1058,8(3) pm; Yb6,081[Si11N20,243]O0,757: a = 974,9(1) pm, c = 1055,7(2) pm; Dy0,33Sm6[Si11N20]N: a = 989,8(1) pm, c = 1078,7(1) pm; Nd7[Si8Al3N20]O: a = 1004,25(9) pm, c = 1095,03(12) pm. Die homootypen Kristallstrukturen aller vier Verbindungen wurden aus Einkristalldaten gelost und in der Raumgruppe P31c mit Z = 2 verfeinert. Die Strukturen sind aus dreidimensionalen Netzwerken eckenverknupfter SiN4- bzw. AlN4-Tetraeder aufgebaut. In den Hohlraumen finden sich Ln3+-Kationen und isolierte O2–-Anionen. Gemas der allgemeinen Formel Ln(6+x/3)[Si(11–y)AlyN(20+x–y)]O(1–x+y) wurde der zuvor von Woike und Jeitschko beschriebene Er6[Si11N20]O-Strukturtyp erweitert. New Representatives of the Er6[Si11N20]O Structure Type. High-Temperature Synthesis and Single-Crystal Structure Refinement of Ln(6+x/3)[Si(11–y)AlyN(20+x–y)]O(1–x+y) with Ln = Nd, Er, Yb, Dy and 0 ≤ x ≤ 3, 0 ≤ y ≤ 3 According to the general formula Ln(6+x/3)[Si(11–y)AlyN(20+x–y)]O(1–x+y) (0 ≤ x ≤ 3, 0 ≤ y ≤ 3) four nitridosilicates, namely Er6[Si11N20]O, Yb6.081[Si11N20.234]O0.757, Dy0.33Sm6[Si11N20]N, and Nd7[Si8Al3N20]O were synthesized in a radiofrequency furnace at temperatures between 1300 and 1650 °C. The homeotypic crystal structures of all four compounds were determined by single-crystal X-ray diffraction. The nitridosilicates are trigonal with the following lattice constants: Er6[Si11N20]O: a = 978.8(4) pm, c = 1058.8(3) pm; Yb6.081[Si11N20.243]O0.757: a = 974.9(1) pm, c = 1055.7(2) pm; Dy0.33Sm6[Si11N20]N: a = 989.8(1) pm, c = 1078.7(1) pm; Nd7[Si8Al3N20]O: a = 1004.25(9) pm, c = 1095.03(12) pm. The crystal structures were solved and refined in the space group P31c with Z = 2. The compounds contain three-dimensional networks built up by corner sharing SiN4 and AlN4 tetrahedra, respectively. The Ln3+ and the “isolated” O2– ions are situated in the voids of the structures. According to Ln(6+x/3)[Si(11–y)AlyN(20+x–y)]O(1–x+y) an extension of the Er6[Si11N20]O structure type has been found.
Optimizing the diagnostic capacity for COVID-19 PCR testing for low resource and high demand settings: The development of information-dependent pooling protocol

Aim To compare different pooling methods in an attempt to improve the COVID-19 PCR diagnostic capacities. Method We developed a novel information-dependent pooling protocol (indept), based on transmission of less informative sequential pools on to the next pooling cycle to maximize savings. We then compared it to the halving, generalized halving, splitting and hypercube protocols in a simulation study, across variety of scenarios. Results All five methods yielded various amount of test savings, which mostly depended on the virus prevalence in the population. In situations of low prevalence (up to 5%), indept had the best performance, requiring on average 20% of tests needed for singular testing across scenarios that were analyzed. Nevertheless, this comes at the expense of speed, with the worst-case scenario of indept protocol requiring up to twice the time needed to test the same number of samples in comparison to the hypercube protocol. In order to offset this, we developed a faster version of the protocol (indeptSp), which minimizes the number of terminal pools and manages to retain savings compared to other protocols, despite marginally longer processing times. Conclusion The increasing demand for more testing globally can benefit from application of pooling, especially in resource-restrained situations of the low- and middle-income countries or situations of high testing demand. Singular testing in situations of low prevalence should be systematically discouraged.