Logic in the Tractatus

I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named. There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably infinite, then the property of being a tautology is \Pi^1_1-complete. But third, it is only granted the assumption of countability that the class of tautologies is \Sigma_1-definable in set theory. Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects

Proceedings of the 5th International Workshop on Reconfigurable Communication-centric Systems on Chip 2010 - ReCoSoC\u2710 - May 17-19, 2010 Karlsruhe, Germany. (KIT Scientific Reports ; 7551)

ReCoSoC is intended to be a periodic annual meeting to expose and discuss gathered expertise as well as state of the art research around SoC related topics through plenary invited papers and posters. The workshop aims to provide a prospective view of tomorrow\u27s challenges in the multibillion transistor era, taking into account the emerging techniques and architectures exploring the synergy between flexible on-chip communication and system reconfigurability

Complexity-reduced hardware-based track-trigger for CMS upgrade

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC) is designed to study the results of proton-proton collisions. The Tracker sub-detector is designed to detect and reconstruct the trajectories of charged particles produced by the collisions. During the lifetime of the CMS detector, there have been several upgrades aimed at increasing the chance of discovering new physics through increased luminosity levels and instrumentation of advanced technology. The High-Luminosity upgrade optimises the LHC to accelerate high-energy particles with an average of 200 proton-proton interactions per bunch crossing. The Level-1 Trigger system promptly analyses and filters collisions using hardware to reduce the data volume in real-time. For the upgrade, the trigger mechanism will use a particle trajectory estimator that discriminates between particles based on their transverse momentum (pT ). Particles with pT ≥ 2 GeV/c will be transmitted to the Level-1 Track-Trigger system for trajectory reconstruction within a fixed 3 μs latency. This thesis presents a novel Hardware-based Multivariate Linear Fitter (MVLF) system focusing on robustness in tracking efficiency and reduction in logic resource usage within the specified latency. The system components are implemented in Field Programmable Gate Arrays (FPGA), targeting 16 nm FinFET UltraScale+ silicon technology. The development was performed using the High-Level Synthesis (HLS) automation tools and the Hardware acceleration platform for Application-Specific Integrated Circuits (ASIC). A firmware demonstrator has been assembled to verify the feasibility and compatibility of the scaled system with the CMS Level-1 Track-Trigger infrastructure. The system’s performance is compared to past and current system developments, and the results are presented accordingly

Aspects of multi-resolutional foveal images for robot vision

Imperial Users onl

Lossy Polynomial Datapath Synthesis

The design of the compute elements of hardware, its datapath, plays a crucial role in determining the speed, area and power consumption of a device. The building blocks of datapath are polynomial in nature. Research into the implementation of adders and multipliers has a long history and developments in this area will continue. Despite such efficient building block implementations, correctly determining the necessary precision of each building block within a design is a challenge. It is typical that standard or uniform precisions are chosen, such as the IEEE floating point precisions. The hardware quality of the datapath is inextricably linked to the precisions of which it is composed. There is, however, another essential element that determines hardware quality, namely that of the accuracy of the components. If one were to implement each of the official IEEE rounding modes, significant differences in hardware quality would be found. But in the same fashion that standard precisions may be unnecessarily chosen, it is typical that components may be constructed to return one of these correctly rounded results, where in fact such accuracy is far from necessary. Unfortunately if a lesser accuracy is permissible then the techniques that exist to reduce hardware implementation cost by exploiting such freedom invariably produce an error with extremely difficult to determine properties. This thesis addresses the problem of how to construct hardware to efficiently implement fixed and floating-point polynomials while exploiting a global error freedom. This is a form of lossy synthesis. The fixed-point contributions include resource minimisation when implementing mutually exclusive polynomials, the construction of minimal lossy components with guaranteed worst case error and a technique for efficient composition of such components. Contributions are also made to how a floating-point polynomial can be implemented with guaranteed relative error.Open Acces

Computational Optimizations for Machine Learning

The present book contains the 10 articles finally accepted for publication in the Special Issue “Computational Optimizations for Machine Learning” of the MDPI journal Mathematics, which cover a wide range of topics connected to the theory and applications of machine learning, neural networks and artificial intelligence. These topics include, among others, various types of machine learning classes, such as supervised, unsupervised and reinforcement learning, deep neural networks, convolutional neural networks, GANs, decision trees, linear regression, SVM, K-means clustering, Q-learning, temporal difference, deep adversarial networks and more. It is hoped that the book will be interesting and useful to those developing mathematical algorithms and applications in the domain of artificial intelligence and machine learning as well as for those having the appropriate mathematical background and willing to become familiar with recent advances of machine learning computational optimization mathematics, which has nowadays permeated into almost all sectors of human life and activity

Sparsity in deep learning: Pruning and growth for efficient inference and training in neural networks

The growing energy and performance costs of deep learning have driven the community to reduce the size of neural networks by selectively pruning components. Similarly to their biological counterparts, sparse networks generalize just as well, sometimes even better than, the original dense networks. Sparsity promises to reduce the memory footprint of regular networks to fit mobile devices, as well as shorten training time for ever growing networks. In this paper, we survey prior work on sparsity in deep learning and provide an extensive tutorial of sparsification for both inference and training. We describe approaches to remove and add elements of neural networks, different training strategies to achieve model sparsity, and mechanisms to exploit sparsity in practice. Our work distills ideas from more than 300 research papers and provides guidance to practitioners who wish to utilize sparsity today, as well as to researchers whose goal is to push the frontier forward. We include the necessary background on mathematical methods in sparsification, describe phenomena such as early structure adaptation, the intricate relations between sparsity and the training process, and show techniques for achieving acceleration on real hardware. We also define a metric of pruned parameter efficiency that could serve as a baseline for comparison of different sparse networks. We close by speculating on how sparsity can improve future workloads and outline major open problems in the field

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4