Miracle-dz/UniFAR-FTUs huggingface dataset:
Monotonicity of solutions for fractional equations with De Giorgi type nonlinearities.

In this paper, we develop a sliding method for the fractional Laplacian. We first obtain the key ingredients needed in the sliding method either in a bounded domain or in the whole space, such as narrow region principles and maximum principles in unbounded domains. Then using semi-linear equations involving the fractional Laplacian in both bounded domains and in the whole space, we illustrate how this new sliding method can be employed to obtain monotonicity of solutions. Some new ideas are introduced. Among which, one is to use Poisson integral representation of $s$-subharmonic functions in deriving the maximum principle, the other is to estimate the singular integrals defining the fractional Laplacians along a sequence of approximate maximum points by using a generalized average inequality. We believe that this new inequality will become a useful tool in analyzing fractional equations.
Spatial variations in the Caspian Sea wave climate in 2002–2013 from satellite altimetry

The core properties of the wave climate and its changes in the Caspian Sea are established in terms of the annual mean significant wave height and its regional changes in 2002-2013 based on the outcome of the satellite altimetry mission JASON-1. Remotely estimated wave heights are validated against properties of the empirical distribution of instrumentally measured wave heights in the southern Caspian Sea and monthly averages of visually observed wave heights at three locations. A correction for systematic differences leads to very good correspondence between monthly averaged in situ and satellite data with a typical root mean square difference of 0.06 m. The average significant wave height in the Caspian Sea is 0.5-0.7 m in the northern basin of the sea, around 1.2 m in large parts of the central and southern basins and reaches up to 1.8 m in the northern segment of the central basin. The basin-wide average wave intensity varied insignificantly in the range of 1.02-1.14 m in 2002-2013. These estimates overestimate the wave heights by about 30% because low wave conditions are ignored. Substantial and statistically significant changes in the wave height occurred in certain areas. The wave height decreased by 0.019 +- 0.007 m/yr in the eastern segment of the central basin and by 0.04 +- 0.04 m/yr in the western segment of the southern basin. These changes can be explained by an increase in the frequency of westerly winds at the expence of southerly winds. Both basin-wide and regional extreme wave heights exhibit large interannual variations but do not show any significant trend. The patterns of changes in mean and extreme wave height are different. The average wave height has increased while the extreme wave height has decreased in the eastern segment of the southern basin.
Trinity of relational quantum dynamics

The problem of time in quantum gravity calls for a relational solution. Using quantum reduction maps, we establish a previously unknown equivalence between three approaches to relational quantum dynamics: 1) relational observables in the clock-neutral picture of Dirac quantization, 2) Page and Wootters' (PW) Schrodinger picture formalism, and 3) the relational Heisenberg picture obtained via symmetry reduction. Constituting three faces of the same dynamics, we call this equivalence the trinity. We develop a quantization procedure for relational Dirac observables using covariant POVMs which encompass non-ideal clocks. The quantum reduction maps reveal this procedure as the quantum analog of gauge-invariantly extending gauge-fixed quantities. We establish algebraic properties of these relational observables. We extend a recent `clock-neutral' approach to changing temporal reference frames, transforming relational observables and states, and demonstrate a clock dependent temporal nonlocality effect. We show that Kuchař's criticism, alleging that the conditional probabilities of the PW formalism violate the constraint, is incorrect. They are a quantum analog of a gauge-fixed description of a gauge-invariant quantity and equivalent to the manifestly gauge-invariant evaluation of relational observables in the physical inner product. The trinity furthermore resolves a previously reported normalization ambiguity and clarifies the role of entanglement in the PW formalism. The trinity finally permits us to resolve Kuchař's criticism that the PW formalism yields wrong propagators by showing how conditional probabilities of relational observables give the correct transition probabilities. Unlike previous proposals, our resolution does not invoke approximations, ideal clocks or ancilla systems, is manifestly gauge-invariant, and easily extends to an arbitrary number of conditionings.
Barcodes as summary of objective function's topology

We apply the canonical forms (barcodes) of gradient Morse complexes to explore topology of loss surfaces. We present a new algorithm for calculations of the objective function's barcodes of minima. Our experiments confirm two principal observations: 1) the barcodes of minima are located in a small lower part of the range of values of loss function of neural networks, 2) an increase of the neural network's depth brings down the minima's barcodes. This has natural implications for the neural network's learning and generalization ability.
Conclusion-Supplement Answer Generation for Non-Factoid Questions

This paper tackles the goal of conclusion-supplement answer generation for non-factoid questions, which is a critical issue in the field of Natural Language Processing (NLP) and Artificial Intelligence (AI), as users often require supplementary information before accepting a conclusion. The current encoder-decoder framework, however, has difficulty generating such answers, since it may become confused when it tries to learn several different long answers to the same non-factoid question. Our solution, called an ensemble network, goes beyond single short sentences and fuses logically connected conclusion statements and supplementary statements. It extracts the context from the conclusion decoder's output sequence and uses it to create supplementary decoder states on the basis of an attention mechanism. It also assesses the closeness of the question encoder's output sequence and the separate outputs of the conclusion and supplement decoders as well as their combination. As a result, it generates answers that match the questions and have natural-sounding supplementary sequences in line with the context expressed by the conclusion sequence. Evaluations conducted on datasets including “Love Advice” and “Arts & Humanities” categories indicate that our model outputs much more accurate results than the tested baseline models do.
Implicit Priors for Knowledge Sharing in Bayesian Neural Networks

Bayesian interpretations of neural network have a long history, dating back to early work in the 1990's and have recently regained attention because of their desirable properties like uncertainty estimation, model robustness and regularisation. We want to discuss here the application of Bayesian models to knowledge sharing between neural networks. Knowledge sharing comes in different facets, such as transfer learning, model distillation and shared embeddings. All of these tasks have in common that learned "features" ought to be shared across different networks. Theoretically rooted in the concepts of Bayesian neural networks this work has widespread application to general deep learning.
Alignment Free and Distortion Robust Iris Recognition

Iris recognition is a reliable personal identification method but there is still much room to improve its accuracy especially in less-constrained situations. For example, free movement of head pose may cause large rotation difference between iris images. And illumination variations may cause irregular distortion of iris texture. To match intra-class iris images with head rotation robustly, the existing solutions usually need a precise alignment operation by exhaustive search within a determined range in iris image preprosessing or brute-force searching the minimum Hamming distance in iris feature matching. In the wild enviroments, iris rotation is of much greater uncertainty than that in constrained situations and exhaustive search within a determined range is impracticable. This paper presents a unified feature-level solution to both alignment free and distortion robust iris recognition in the wild. A new deep learning based method named Alignment Free Iris Network (AFINet) is proposed, which utilizes a trainable VLAD (Vector of Locally Aggregated Descriptors) encoder called NetVLAD [18] to decouple the correlations between local representations and their spatial positions. And deformable convolution [5] is leveraged to overcome iris texture distortion by dense adaptive sampling. The results of extensive experiments on three public iris image databases and the simulated degradation databases show that AFINet significantly outperforms state-of-art iris recognition methods.
Uncovering the orbit of the hercules dwarf galaxy

We present new chemo-kinematics of the Hercules dwarf galaxy based on Keck II-DEIMOS spectroscopy. Our 21 confirmed members, including 9 newly confirmed members, have a systemic velocity of vHerc = 46.4 ± 1.3 km s−1 and a velocity dispersion $\sigma _{v,\mathrm{Herc}}=4.4^{+1.4}_{-1.2}$ km s−1, consistent with previous studies. From the strength of the Ca ii triplet, we obtain a metallicity of [Fe/H] = −2.48 ± 0.19 dex and dispersion of $\sigma _{\rm {[Fe/H]}}= 0.63^{+0.18}_{-0.13}$ dex. This result is within 1σ of previous measurements, and makes Hercules a particularly metal-poor galaxy, placing it slightly below the standard mass–metallicity relation. Previous photometric and spectroscopic evidence suggests that Hercules is tidally disrupting and may be on a highly radial orbit. From our identified members, we measure no significant velocity gradient. By cross-matching with the second Gaia data release, we determine an uncertainty-weighted mean proper motion of $\mu _{\alpha }^*=\mu _{\alpha }\cos (\delta)=-0.153\pm {0.074}$ mas yr−1, μδ = −0.397 ± 0.063 mas yr−1. This proper motion is slightly misaligned with the elongation of Hercules, in contrast to models which suggest that any tidal debris should be well aligned with the orbital path. Future observations may resolve this tension.
Automated curriculum generation for Policy Gradients from Demonstrations

In this paper, we present a technique that improves the process of training an agent (using RL) for instruction following. We develop a training curriculum that uses a nominal number of expert demonstrations and trains the agent in a manner that draws parallels from one of the ways in which humans learn to perform complex tasks, i.e by starting from the goal and working backwards. We test our method on the BabyAI platform and show an improvement in sample efficiency for some of its tasks compared to a PPO (proximal policy optimization) baseline.
An Attention-Based Speaker Naming Method for Online Adaptation in Non-Fixed Scenarios

A speaker naming task, which finds and identifies the active speaker in a certain movie or drama scene, is crucial for dealing with high-level video analysis applications such as automatic subtitle labeling and video summarization. Modern approaches have usually exploited biometric features with a gradient-based method instead of rule-based algorithms. In a certain situation, however, a naive gradient-based method does not work efficiently. For example, when new characters are added to the target identification list, the neural network needs to be frequently retrained to identify new people and it causes delays in model preparation. In this paper, we present an attention-based method which reduces the model setup time by updating the newly added data via online adaptation without a gradient update process. We comparatively analyzed with three evaluation metrics(accuracy, memory usage, setup time) of the attention-based method and existing gradient-based methods under various controlled settings of speaker naming. Also, we applied existing speaker naming models and the attention-based model to real video to prove that our approach shows comparable accuracy to the existing state-of-the-art models and even higher accuracy in some cases.
Quantized deep learning models on low-power edge devices for robotic systems

In this work, we present a quantized deep neural network deployed on a low-power edge device, inferring learned motor-movements of a suspended robot in a defined space. This serves as the fundamental building block for the original setup, a robotic system for farms or greenhouses aimed at a wide range of agricultural tasks. Deep learning on edge devices and its implications could have a substantial impact on farming systems in the developing world, leading not only to sustainable food production and income, but also increased data privacy and autonomy.
Effective Hamiltonians for interacting superconducting qubits: local basis reduction and the Schrieffer–Wolff transformation

An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum information. Despite advances in numerical methods to simulate the spectral properties of multi-element superconducting circuits (Yurke B and Denker J S 1984 Phys. Rev. A 29 1419, Reiter F and Sørensen A S 2012 Phys. Rev. A 85 032111 and Amin M H et al 2012 Phys. Rev. A 86 052314), the literature lacks a consistent and effective method of determining the effective qubit Hamiltonian. Here we address this problem by introducing a novel local basis reduction method. This method does not require any ad hoc assumption on the structure of the Hamiltonian such as its linear response to applied fields. We numerically benchmark the local basis reduction method against other Hamiltonian reduction methods in the literature and report specific examples of superconducting qubits, including the capacitively-shunted flux qubit, where the standard reduction approaches fail. By combining the local basis reduction method with the Schrieffer–Wolff transformation we further extend its applicability to systems of interacting qubits and use it to extract both non-stoquastic two-qubit Hamiltonians and three-local interaction terms in three-qubit Hamiltonians.
Capacity of the covariance perceptron

The classical perceptron is a simple neural network that performs a binary classification by a linear mapping between static inputs and outputs and application of a threshold. For small inputs, neural networks in a stationary state also perform an effectively linear input–output transformation, but of an entire time series. Choosing the temporal mean of the time series as the feature for classification, the linear transformation of the network with subsequent thresholding is equivalent to the classical perceptron. Here we show that choosing covariances of time series as the feature for classification maps the neural network to what we call a ‘covariance perceptron’; a mapping between covariances that is bilinear in terms of weights. By extending Gardner’s theory of connections to this bilinear problem, using a replica symmetric mean-field theory, we compute the pattern and information capacities of the covariance perceptron in the infinite-size limit. Closed-form expressions reveal superior pattern capacity in the binary classification task compared to the classical perceptron in the case of a high-dimensional input and low-dimensional output. For less convergent networks, the mean perceptron classifies a larger number of stimuli. However, since covariances span a much larger input and output space than means, the amount of stored information in the covariance perceptron exceeds the classical counterpart. For strongly convergent connectivity it is superior by a factor equal to the number of input neurons. Theoretical calculations are validated numerically for finite size systems using a gradient-based optimization of a soft-margin, as well as numerical solvers for the NP hard quadratically constrained quadratic programming problem, to which training can be mapped.
Novel immunisation strategies against Salmonella

There are currently two vaccines licensed for use against Salmonella enterica serovar Typhi (S. typhi) infection, namely the live attenuated vaccine and the Vi polysaccharide sub-unit vaccine. Both vaccines induce protective immune responses, however they do so with variable efficacy. Considerable progress has been made in the development of alternative live attenuated S. typhi vaccines, however little progress has been made in the development of alternative sub-unit vaccines. Considerable progress has also been made in the comparatively new field of DNA vaccines, however very little progress has been made in their application to Salmonella. This thesis presents two novel immunisation strategies against Salmonella enterica serovar Typhimurium (S. typhimurium) in the mouse model. Firstly, mice immunised with multiple antigens in the form of a DNA vaccine have been shown to develop specific humoral and cellular responses to proteins encoded within the vaccine. Secondly, it has been shown that immunisation with multiple cytosolic antigens (CA) of S. typhimurium SL1344, formulated with the adjuvant dimethyl dioctadecyl arnmoniumbromide (DDA), induces strong humoral and cellular responses. These responses have been characterised, and their ability to confer protection on mice challenged with a lethal dose of S. typhimurium SL 1344 has been investigated. The aim of DNA vaccination is to induce immune responses to protein antigens expressed in vivo by injecting plasmid DNA encoding the antigen sequence. Expression library immunisation (ELI) is a new technique that draws on DNA immunisation and can be developed to identify the key antigens of a pathogen that confer protection. ELI has previously been used in a number of disease models in mice and has been used in this thesis as a means of inducing immune responses against an unspecified subset of bacterial antigens. An expression library (EL) of S. typhimurium SL1344 was constructed using a mammalian expression vector encoding EGFP. The expression of S. typhimurium SL1344 antigens forming fusion proteins with EGFP was visualised as
Testing the relativistic Doppler boost hypothesis for supermassive binary black holes candidates via broad emission line profiles

Optical periodicity QSOs found by transient surveys are suggested to be subparsec supermassive binary black holes (BBHs). An intriguing interpretation for the periodicity of some of those QSOs is that the continuum is radiated from the accretion disc associated with the BBH secondary component and modulated by the periodical rotation of the secondary via Doppler-boost effect. Close to edge-on orbital orientation can lead to more significant Doppler-boost effect and thus are preferred for these systems, which is distinct from those normal type-1 QSOs with more or less face-on orientations. Therefore, the profiles of broad lines emitted from these Doppler-modulated systems may be significantly different from other systems that are not Doppler modulated. We investigate the properties of the broad emission lines of optical-periodicity QSOs, including both a sample of QSOs that can be interpreted by the Doppler-modulated effects and a sample that cannot. We find that there is no obvious difference in the profiles and other properties of various (stacked) broad emission lines of these two samples, though a simple broad line region model would suggest significant differences. Our finding raises a challenge to the Doppler boost hypothesis for some of those BBHs candidates with optical periodicity.
A Machine Learning Approach to Adaptive Robust Utility Maximization and Hedging

We investigate the adaptive robust control framework for portfolio optimization and loss-based hedging under drift and volatility uncertainty. Adaptive robust problems offer many advantages but require handling a double optimization problem (infimum over market measures, supremum over the control) at each instance. Moreover, the underlying Bellman equations are intrinsically multi-dimensional. We propose a novel machine learning approach that solves for the local saddle-point at a chosen set of inputs and then uses a nonparametric (Gaussian process) regression to obtain a functional representation of the value function. Our algorithm resembles control randomization and regression Monte Carlo techniques but also brings multiple innovations, including adaptive experimental design, separate surrogates for optimal control and the local worst-case measure, and computational speed-ups for the sup-inf optimization. Thanks to the new scheme we are able to consider settings that have been previously computationally intractable and provide several new financial insights about learning and optimal trading under unknown market parameters. In particular, we demonstrate the financial advantages of adaptive robust framework compared to adaptive and static robust alternatives.
Multi-version Indexing in Flash-based Key-Value Stores

Maintaining multiple versions of data is popular in key-value stores since it increases concurrency and improves performance. However, designing a multi-version key-value store entails several challenges, such as additional capacity for storing extra versions and an indexing mechanism for mapping versions of a key to their values. We present SkimpyFTL, a FTL-integrated multi-version key-value store that exploits the remap-on-write property of flash-based SSDs for multi-versioning and provides a tradeoff between memory capacity and lookup latency for indexing.
Quadratic Q-network for Learning Continuous Control for Autonomous Vehicles

Reinforcement Learning algorithms have recently been proposed to learn time-sequential control policies in the field of autonomous driving. Direct applications of Reinforcement Learning algorithms with discrete action space will yield unsatisfactory results at the operational level of driving where continuous control actions are actually required. In addition, the design of neural networks often fails to incorporate the domain knowledge of the targeting problem such as the classical control theories in our case. In this paper, we propose a hybrid model by combining Q-learning and classic PID (Proportion Integration Differentiation) controller for handling continuous vehicle control problems under dynamic driving environment. Particularly, instead of using a big neural network as Q-function approximation, we design a Quadratic Q-function over actions with multiple simple neural networks for finding optimal values within a continuous space. We also build an action network based on the domain knowledge of the control mechanism of a PID controller to guide the agent to explore optimal actions more efficiently.We test our proposed approach in simulation under two common but challenging driving situations, the lane change scenario and ramp merge scenario. Results show that the autonomous vehicle agent can successfully learn a smooth and efficient driving behavior in both situations.