This paper gives a localized method for the multi-commodity flow problem. We relax both the capacity constraints and flow conservation constraints, and introduce a congestion function $psi$ for each arc and $height$ function $h$ for each vertex and c
ommodity. If the flow exceeds the capacity on arc $a$, arc $a$ would have a congestion cost. If the flow into the vertex $i$ is not equal to that out of the vertex for commodity $k$, vertex $i$ would have a height, which is positively related to the difference between the amount of the commodity $k$ into the vertex $i$ and that out of the vertex. Based on the height function $h$ and the congestion function $psi$, a new conception, stable pseudo-flow, is introduced, which satisfies the following conditions: ($mathrm{i}$) for any used arc of commodity $k$, the height difference between vertex $i$ and vertex $j$ is equal to the congestion of arc $(i,j)$; ($mathrm{ii}$) for any unused arc of commodity $k$, the height difference between vertex $i$ and vertex $j$ is less than or equal to the congestion of arc $(i,j)$. If the stable pseudo-flow is a nonzero-stable pseudo-flow, there exists no feasible solution for the multi-commodity flow problem; if the stable pseudo-flow is a zero-stable pseudo-flow, there exists feasible solution for the multi-commodity flow problem and the zero-stable pseudo-flow is the feasible solution. Besides, a non-linear description of the multi-commodity flow problem is given, whose solution is stable pseudo-flow. And the non-linear description could be rewritten as convex quadratic programming with box constraints. Rather than examine the entire network to find path, the conclusion in this paper shows that the multi-commodity flow problem could be solved in a localized manner by looking only at the vertex and its neighbors.
This paper surveys and organizes research works in a new paradigm in natural language processing, which we dub prompt-based learning. Unlike traditional supervised learning, which trains a model to take in an input x and predict an output y as P(y|x)
, prompt-based learning is based on language models that model the probability of text directly. To use these models to perform prediction tasks, the original input x is modified using a template into a textual string prompt x that has some unfilled slots, and then the language model is used to probabilistically fill the unfilled information to obtain a final string x, from which the final output y can be derived. This framework is powerful and attractive for a number of reasons: it allows the language model to be pre-trained on massive amounts of raw text, and by defining a new prompting function the model is able to perform few-shot or even zero-shot learning, adapting to new scenarios with few or no labeled data. In this paper we introduce the basics of this promising paradigm, describe a unified set of mathematical notations that can cover a wide variety of existing work, and organize existing work along several dimensions, e.g.the choice of pre-trained models, prompts, and tuning strategies. To make the field more accessible to interested beginners, we not only make a systematic review of existing works and a highly structured typology of prompt-based concepts, but also release other resources, e.g., a website http://pretrain.nlpedia.ai/ including constantly-updated survey, and paperlist.
With new emerging technologies, such as satellites and drones, archaeologists collect data over large areas. However, it becomes difficult to process such data in time. Archaeological data also have many different formats (images, texts, sensor data)
and can be structured, semi-structured and unstructured. Such variety makes data difficult to collect, store, manage, search and analyze effectively. A few approaches have been proposed, but none of them covers the full data lifecycle nor provides an efficient data management system. Hence, we propose the use of a data lake to provide centralized data stores to host heterogeneous data, as well as tools for data quality checking, cleaning, transformation, and analysis. In this paper, we propose a generic, flexible and complete data lake architecture. Our metadata management system exploits goldMEDAL, which is the most complete metadata model currently available. Finally, we detail the concrete implementation of this architecture dedicated to an archaeological project.
Dirac semimetal (DSM) is a phase of matter, whose elementary excitation is described by the relativistic Dirac equation. Its parity-time symmetry enforces the linear-dispersed Dirac cone in the momentum space to be non-chiral, leading to surface stat
es connected adiabatically to a topologically trivial surface state. Inspired by the flavor symmetry in particle physics, we theoretically propose a massless chiral Dirac equation linking two Weyl fields with the identical chirality by assuming SU(2) isospin symmetry, independent of the space-time rotation exchanging the two fields. Dramatically, such symmetry is hidden in certain solid-state spin-1/2 systems with negligible spin-orbit coupling, where the spin degree of freedom is decoupled with the lattice. Therefore, it cannot be explained by the conventional (magnetic) space group framework. The corresponding system is called chiral DSM. The four-fold degenerate Dirac fermion manifests linear dispersion and a Chern number of +2/-2, leading to a robust network of topologically protected Fermi arcs throughout the Brillouin zone. For material realization, we show that the transition-metal chalcogenide CoNb3S6 with experimentally confirmed collinear antiferromagnetic order is ideal for chiral DSM. Our work unprecedentedly reveals a condensed-matter counterpart of the flavor symmetry in particle physics, leading to further possibilities of emergent phenomena in quantum materials.
Alchemical binding free energy (BFE) calculations offer an efficient and thermodynamically rigorous approach to in silico binding affinity predictions. As a result of decades of methodological improvements and recent advances in computer technology,
alchemical BFE calculations are now widely used in drug discovery research. They help guide the prioritization of candidate drug molecules by predicting their binding affinities for a biomolecular target of interest (and potentially selectivity against undesirable anti-targets). Statistical variance associated with such calculations, however, may undermine the reliability of their predictions, introducing uncertainty both in ranking candidate molecules and in benchmarking their predictive accuracy. Here, we present a computational method that substantially improves the statistical precision in BFE calculations for a set of ligands binding to a common receptor by dynamically allocating computational resources to different BFE calculations according to an optimality objective established in a previous work from our group and extended in this work. Our method, termed Network Binding Free Energy (NetBFE), performs adaptive binding free energy calculations in iterations, re-optimizing the allocations in each iteration based on the statistical variances estimated from previous iterations. Using examples of NetBFE calculations for protein-binding of congeneric ligand series, we demonstrate that NetBFE approaches the optimal allocation in a small number (<= 5) of iterations and that NetBFE reduces the statistical variance in the binding free energy estimates by approximately a factor of two when compared to a previously published and widely used allocation method at the same total computational cost.
We summarize here a paper published in 2021 in the DOLAP international workshop DOLAP associated with the EDBT and ICDT conferences. We propose goldMEDAL, a generic metadata model for data lakes based on four concepts and a three-level modeling: conceptual, logical and physical.
A wide variety of NLP applications, such as machine translation, summarization, and dialog, involve text generation. One major challenge for these applications is how to evaluate whether such generated texts are actually fluent, accurate, or effectiv
e. In this work, we conceptualize the evaluation of generated text as a text generation problem, modeled using pre-trained sequence-to-sequence models. The general idea is that models trained to convert the generated text to/from a reference output or the source text will achieve higher scores when the generated text is better. We operationalize this idea using BART, an encoder-decoder based pre-trained model, and propose a metric BARTScore with a number of variants that can be flexibly applied in an unsupervised fashion to evaluation of text from different perspectives (e.g. informativeness, fluency, or factuality). BARTScore is conceptually simple and empirically effective. It can outperform existing top-scoring metrics in 16 of 22 test settings, covering evaluation of 16 datasets (e.g., machine translation, text summarization) and 7 different perspectives (e.g., informativeness, factuality). Code to calculate BARTScore is available at https://github.com/neulab/BARTScore, and we have released an interactive leaderboard for meta-evaluation at http://explainaboard.nlpedia.ai/leaderboard/task-meval/ on the ExplainaBoard platform, which allows us to interactively understand the strengths, weaknesses, and complementarity of each metric.
State-of-the-art summarization systems are trained and evaluated on massive datasets scraped from the web. Despite their prevalence, we know very little about the underlying characteristics (data noise, summarization complexity, etc.) of these datase
ts, and how these affect system performance and the reliability of automatic metrics like ROUGE. In this study, we manually analyze 600 samples from three popular summarization datasets. Our study is driven by a six-class typology which captures different noise types (missing facts, entities) and degrees of summarization difficulty (extractive, abstractive). We follow with a thorough analysis of 27 state-of-the-art summarization models and 5 popular metrics, and report our key insights: (1) Datasets have distinct data quality and complexity distributions, which can be traced back to their collection process. (2) The performance of models and reliability of metrics is dependent on sample complexity. (3) Faithful summaries often receive low scores because of the poor diversity of references. We release the code, annotated data and model outputs.
We report symmetry-breaking and restoring bifurcations of solitons in a fractional Schr{o}dinger equation with the cubic or cubic-quintic (CQ) nonlinearity and a parity-time (PT)-symmetric potential, which may be realized in optical cavities. Soliton
s are destabilized at the bifurcation point, and, in the case of the CQ nonlinearity, the stability is restored by an inverse bifurcation. Two mutually-conjugate branches of ghost states (GSs), with complex propagation constants, are created by the bifurcation, solely in the case of the fractional diffraction. While GSs are not true solutions, direct simulations confirm that their shapes and results of their stability analysis provide a blueprint for the evolution of genuine localized modes in the system.
The Gini index is a popular inequality measure with many applications in social and economic studies. This paper studies semiparametric inference on the Gini indices of two semicontinuous populations. We characterize the distribution of each semicont
inuous population by a mixture of a discrete point mass at zero and a continuous skewed positive component. A semiparametric density ratio model is then employed to link the positive components of the two distributions. We propose the maximum empirical likelihood estimators of the two Gini indices and their difference, and further investigate the asymptotic properties of the proposed estimators. The asymptotic results enable us to construct confidence intervals and perform hypothesis tests for the two Gini indices and their difference. We show that the proposed estimators are more efficient than the existing fully nonparametric estimators. The proposed estimators and the asymptotic results are also applicable to cases without excessive zero values. Simulation studies show the superiority of our proposed method over existing methods. Two real-data applications are presented using the proposed methods.
