Local Well-Posedness of Skew Mean Curvature Flow for Small Data in $$d\ge 4$$ Dimensions

The skew mean curvature flow is an evolution equation for d dimensional manifolds embedded in $${{\mathbb {R}}}^{d+2}$$ R d + 2 (or more generally, in a Riemannian manifold). It can be viewed as a Schrödinger analogue of the mean curvature flow, or alternatively as a quasilinear version of the Schrödinger Map equation. In this article, we prove small data local well-posedness in low-regularity Sobolev spaces for the skew mean curvature flow in dimension $$d\ge 4$$ d ≥ 4 .

Inducing Vascular Grammars for Anomaly Classification in Brain Angiograms

As machine learning is used to make strides in med- ical diagnostics, few methods provide heuristics from which human doctors can learn directly. This work introduces a method for leveraging human observable structures, such as macro scale vascular formations, for producing assessments of medical conditions with rela- tively few training cases, and uncovering patterns that are potential diagnostic aids. The approach draws on shape grammars, a rule-based technique, pioneered in design and architecture, and accelerated through a re- cursive sub-graph mining algorithm. The distribution of rule instances in the data from which they are in- duced is then used as an intermediary representation en- abling common classification and anomaly detection ap- proaches to identify indicative rules with relatively small data sets. The method is applied to 7 Tesla time-of- flight (TOF) angiography MRI (n = 54) of human brain vasculature. The data were segmented and induced to generate representative grammar rules. Ensembles of rules were isolated to implicate vascular conditions reli- ably. This application demonstrates the power of auto- mated structured intermediary representations for as- sessing nuanced biological form relationships, and the strength of shape grammars, in particular for identify- ing indicative patterns in complex vascular networks.

Probabilistic Deterministic Finite Automata and Recurrent Networks, Revisited

Reservoir computers (RCs) and recurrent neural networks (RNNs) can mimic any finite-state automaton in theory, and some workers demonstrated that this can hold in practice. We test the capability of generalized linear models, RCs, and Long Short-Term Memory (LSTM) RNN architectures to predict the stochastic processes generated by a large suite of probabilistic deterministic finite-state automata (PDFA) in the small-data limit according to two metrics: predictive accuracy and distance to a predictive rate-distortion curve. The latter provides a sense of whether or not the RNN is a lossy predictive feature extractor in the information-theoretic sense. PDFAs provide an excellent performance benchmark in that they can be systematically enumerated, the randomness and correlation structure of their generated processes are exactly known, and their optimal memory-limited predictors are easily computed. With less data than is needed to make a good prediction, LSTMs surprisingly lose at predictive accuracy, but win at lossy predictive feature extraction. These results highlight the utility of causal states in understanding the capabilities of RNNs to predict.

A Survey on LoRaWAN Technology: Recent Trends, Opportunities, Simulation Tools and Future Directions

Low-power wide-area network (LPWAN) technologies play a pivotal role in IoT applications, owing to their capability to meet the key IoT requirements (e.g., long range, low cost, small data volumes, massive device number, and low energy consumption). Between all obtainable LPWAN technologies, long-range wide-area network (LoRaWAN) technology has attracted much interest from both industry and academia due to networking autonomous architecture and an open standard specification. This paper presents a comparative review of five selected driving LPWAN technologies, including NB-IoT, SigFox, Telensa, Ingenu (RPMA), and LoRa/LoRaWAN. The comparison shows that LoRa/LoRaWAN and SigFox surpass other technologies in terms of device lifetime, network capacity, adaptive data rate, and cost. In contrast, NB-IoT technology excels in latency and quality of service. Furthermore, we present a technical overview of LoRa/LoRaWAN technology by considering its main features, opportunities, and open issues. We also compare the most important simulation tools for investigating and analyzing LoRa/LoRaWAN network performance that has been developed recently. Then, we introduce a comparative evaluation of LoRa simulators to highlight their features. Furthermore, we classify the recent efforts to improve LoRa/LoRaWAN performance in terms of energy consumption, pure data extraction rate, network scalability, network coverage, quality of service, and security. Finally, although we focus more on LoRa/LoRaWAN issues and solutions, we introduce guidance and directions for future research on LPWAN technologies.

A sparse modeling for small data: Case studies in controlled syntheses of 2D materials

Data-scientific approaches have permeated in chemistry and materials science. In general, these approaches are not easily applied to small data, such as experimental data in laboratories. Our group has focused...

GOOD AND BAD SOCIOLOGY: DOES TOPIC MODELLING MAKE A DIFFERENCE?

The changing social reality, which is increasingly digitally networked, requires new research methods capable of analysing large bodies of data (including textual data). This development poses a challenge for sociology, whose ambition is primarily to describe and explain social reality. As traditional sociological research methods focus on analysing relatively small data, the existential challenge of today involves the need to embrace new methods and techniques, which enable valuable insights into big volumes of data at speed. One such emerging area of investigation involves the application of Natural Language Processing and Machine-Learning to text mining, which allows for swift analyses of vast bodies of textual content. The paper’s main aim is to probe whether such a novel approach, namely, topic modelling based on Latent Dirichlet Allocation (LDA) algorithm, can find meaningful applications within sociology and whether its adaptation makes sociology perform its tasks better. In order to outline the context of the applicability of LDA in the social sciences and humanities, an analysis of abstracts of articles published in journals indexed in Elsevier’s Scopus database on topic modelling was conducted. This study, based on 1,149 abstracts, showed not only the diversity of topics undertaken by researchers but helped to answer the question of whether sociology using topic modelling is “good” sociology in the sense that it provides opportunities for exploration of topic areas and data that would not otherwise be undertaken.