skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: What is a combinatorial interpretation?
In this survey we discuss the notion of combinatorial interpretation in the context of Algebraic Combinatorics and related areas. We approach the subject from the Computational Complexity perspective. We review many examples, state a workable definition, discuss many open problems, and present recent results on the subject.  more » « less
Award ID(s):
2007891
PAR ID:
10379501
Author(s) / Creator(s):
Date Published:
Journal Name:
Open Problem in Algebraic Combinatorics
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted, but the approach extends naturally to other interacting lattice models with time-dependent driving. Although trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy can be beneficial. 
    more » « less
  2. null (Ed.)
    Subject categories of scholarly papers generally refer to the knowledge domain(s) to which the papers belong, examples being computer science or physics. Subject category classification is a prerequisite for bibliometric studies, organizing scientific publications for domain knowledge extraction, and facilitating faceted searches for digital library search engines. Unfortunately, many academic papers do not have such information as part of their metadata. Most existing methods for solving this task focus on unsupervised learning that often relies on citation networks. However, a complete list of papers citing the current paper may not be readily available. In particular, new papers that have few or no citations cannot be classified using such methods. Here, we propose a deep attentive neural network (DANN) that classifies scholarly papers using only their abstracts. The network is trained using nine million abstracts from Web of Science (WoS). We also use the WoS schema that covers 104 subject categories. The proposed network consists of two bi-directional recurrent neural networks followed by an attention layer. We compare our model against baselines by varying the architecture and text representation. Our best model achieves micro- F 1 measure of 0.76 with F 1 of individual subject categories ranging from 0.50 to 0.95. The results showed the importance of retraining word embedding models to maximize the vocabulary overlap and the effectiveness of the attention mechanism. The combination of word vectors with TFIDF outperforms character and sentence level embedding models. We discuss imbalanced samples and overlapping categories and suggest possible strategies for mitigation. We also determine the subject category distribution in CiteSeerX by classifying a random sample of one million academic papers. 
    more » « less
  3. Information extraction (IE) in scientific literature has facilitated many down-stream knowledge-driven tasks. Ope-nIE, which does not require any relation schema but identifies a relational phrase to describe the relationship between a subject and an object, is being a trending topic of IE in sciences. The subjects, objects, and relations are often multiword expressions, which brings challenges for methods to identify the boundaries of the expressions given very limited or even no training data. In this work, we present a set of rules for extracting structured information based on dependency parsing that can be applied to any scientific dataset requiring no expert's annotation. Results on novel datasets show the effectiveness of the proposed method. We discuss negative results as well. 
    more » « less
  4. All biological systems are subject to perturbations arising from thermal fluctuations, external environments, or mutations. Yet, while biological systems consist of thousands of interacting components, recent high-throughput experiments have shown that their response to perturbations is surprisingly low dimensional: confined to only a few stereotyped changes out of the many possible. In this review, we explore a unifying dynamical systems framework—soft modes—to explain and analyze low dimensionality in biology, from molecules to ecosystems. We argue that this soft mode framework makes nontrivial predictions that generalize classic ideas from developmental biology to disparate systems, namely phenocopying, dual buffering, and global epistasis. While some of these predictions have been borne out in experiments, we discuss how soft modes allow for a surprisingly far-reaching and unifying framework in which to analyze data from protein biophysics to microbial ecology. 
    more » « less
  5. Global and team science approaches are on the rise, as is attention to the network underpinnings of gender disparities in scientific collaboration. Many network studies of men’s and women’s collaboration rely on bounded case studies of single disciplines and/or single countries and limited measures related to the collaborative process. We deploy network analysis on the scholarly database Scopus to gain insight into gender inequity across regions and subject areas and to better understand contextual underpinnings of stagnancy. Using a dataset of over 1.2 million authors and 144 million collaborative relationships, we capture international and unbounded co-authorship networks that include intra- and inter-disciplinary co-authorship ties across time (2009–2013). We describe how gender informs structural features and status differences in network relationships, focusing on men and women authors in 16 region-subject pairs. We pay particular attention to how connected authors are (first- and second-order degree centrality), attributes of authors’ collaborative relationships (including the “quality” and other characteristics of these ties), tendencies towards gender homophily (proportion of same-gender ties), and the nature of men’s and women’s interdisciplinary and international reach. Men have more advantageous first-order connections, yet second-order collaborative profiles look more similar. Men and women exhibit homophilous attachment to authors of the same gender, consistent over time. There is notable variation in the level of gender disparity within subjects across countries. We discuss this variation in the context of global trends in men’s and women’s scientific participation and cultural- and country-level influences on the organization and production of science. 
    more » « less