Singular Thought

A singular thought can be characterized as a thought which is directed at just one object. The term ‘thought’ can apply to episodes of thinking, or to the content of the episode (what is thought). This paper argues that episodes of thinking can be just as singular, in the above sense, when they are directed at things that do not exist as when they are directed at things that do exist. In this sense, then, singular thoughts are not object-dependent

NeuTM: A Neural Network-based Framework for Traffic Matrix Prediction in SDN

This paper presents NeuTM, a framework for network Traffic Matrix (TM) prediction based on Long Short-Term Memory Recurrent Neural Networks (LSTM RNNs). TM prediction is defined as the problem of estimating future network traffic matrix from the previous and achieved network traffic data. It is widely used in network planning, resource management and network security. Long Short-Term Memory (LSTM) is a specific recurrent neural network (RNN) architecture that is well-suited to learn from data and classify or predict time series with time lags of unknown size. LSTMs have been shown to model long-range dependencies more accurately than conventional RNNs. NeuTM is a LSTM RNN-based framework for predicting TM in large networks. By validating our framework on real-world data from GEEANT network, we show that our model converges quickly and gives state of the art TM prediction performance.Comment: Submitted to NOMS18. arXiv admin note: substantial text overlap with arXiv:1705.0569

A Long Short-Term Memory Recurrent Neural Network Framework for Network Traffic Matrix Prediction

Network Traffic Matrix (TM) prediction is defined as the problem of estimating future network traffic from the previous and achieved network traffic data. It is widely used in network planning, resource management and network security. Long Short-Term Memory (LSTM) is a specific recurrent neural network (RNN) architecture that is well-suited to learn from experience to classify, process and predict time series with time lags of unknown size. LSTMs have been shown to model temporal sequences and their long-range dependencies more accurately than conventional RNNs. In this paper, we propose a LSTM RNN framework for predicting short and long term Traffic Matrix (TM) in large networks. By validating our framework on real-world data from GEANT network, we show that our LSTM models converge quickly and give state of the art TM prediction performance for relatively small sized models.Comment: Submitted for peer review. arXiv admin note: text overlap with arXiv:1402.1128 by other author

NeuRoute: Predictive Dynamic Routing for Software-Defined Networks

This paper introduces NeuRoute, a dynamic routing framework for Software Defined Networks (SDN) entirely based on machine learning, specifically, Neural Networks. Current SDN/OpenFlow controllers use a default routing based on Dijkstra algorithm for shortest paths, and provide APIs to develop custom routing applications. NeuRoute is a controller-agnostic dynamic routing framework that (i) predicts traffic matrix in real time, (ii) uses a neural network to learn traffic characteristics and (iii) generates forwarding rules accordingly to optimize the network throughput. NeuRoute achieves the same results as the most efficient dynamic routing heuristic but in much less execution time.Comment: Accepted for CNSM 201

The Rule-Following Paradox and the Impossibility of Private Rule-Following

Kripke’s version of Wittgenstein’s rule-following paradox has been influential. My concern is with how it—and Wittgenstein’s views more generally—have been perceived as undercutting the individualistic picture of mathematical practice: the view that individuals—Robinson Crusoes—can, entirely independently of a community, engage in cogent mathematics, and indeed (more generally) have “private languages.” What has been denied is that phrases like “correctly counting” can be applied to such individuals because these normative notions (so the Wittgensteinian analysis is taken to show) can only be applied cogently in a context involving community standards. I attempt to show that this shocking corollary doesn’t follow even if Kripke’s Wittgensteinian objections to dispositional approaches to rule-following are largely right. My reason for claiming this is that there is another (“sceptical”) solution to the rule-following paradox, one that doesn’t favor community standards over individual ones. Furthermore, it doesn’t replace truth conditions with assertability conditions; and this latter maneuver is essential to Kripke’s sceptical solution favoring the community over the individual

From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe