Differential qd algorithm with shifts for rank-structured matrices

Although QR iterations dominate in eigenvalue computations, there are several important cases when alternative LR-type algorithms may be preferable. In particular, in the symmetric tridiagonal case where differential qd algorithm with shifts (dqds) proposed by Fernando and Parlett enjoys often faster convergence while preserving high relative accuracy (that is not guaranteed in QR algorithm). In eigenvalue computations for rank-structured matrices QR algorithm is also a popular choice since, in the symmetric case, the rank structure is preserved. In the unsymmetric case, however, QR algorithm destroys the rank structure and, hence, LR-type algorithms come to play once again. In the current paper we discover several variants of qd algorithms for quasiseparable matrices. Remarkably, one of them, when applied to Hessenberg matrices becomes a direct generalization of dqds algorithm for tridiagonal matrices. Therefore, it can be applied to such important matrices as companion and confederate, and provides an alternative algorithm for finding roots of a polynomial represented in the basis of orthogonal polynomials. Results of preliminary numerical experiments are presented

Generation of Application Specific Hardware Extensions for Hybrid Architectures: The Development of PIRANHA - A GCC Plugin for High-Level-Synthesis

Architectures combining a field programmable gate array (FPGA) and a general-purpose processor on a single chip became increasingly popular in recent years. On the one hand, such hybrid architectures facilitate the use of application specific hardware accelerators that improve the performance of the software on the host processor. On the other hand, it obliges system designers to handle the whole process of hardware/software co-design. The complexity of this process is still one of the main reasons, that hinders the widespread use of hybrid architectures. Thus, an automated process that aids programmers with the hardware/software partitioning and the generation of application specific accelerators is an important issue. The method presented in this thesis neither requires restrictions of the used high-level-language nor special source code annotations. Usually, this is an entry barrier for programmers without deeper understanding of the underlying hardware platform. This thesis introduces a seamless programming flow that allows generating hardware accelerators for unrestricted, legacy C code. The implementation consists of a GCC plugin that automatically identifies application hot-spots and generates hardware accelerators accordingly. Apart from the accelerator implementation in a hardware description language, the compiler plugin provides the generation of a host processor interfaces and, if necessary, a prototypical integration with the host operating system. An evaluation with typical embedded applications shows general benefits of the approach, but also reveals limiting factors that hamper possible performance improvements

Configraphics:

This dissertation reports a PhD research on mathematical-computational models, methods, and techniques for analysis, synthesis, and evaluation of spatial configurations in architecture and urban design. Spatial configuration is a technical term that refers to the particular way in which a set of spaces are connected to one another as a network. Spatial configuration affects safety, security, and efficiency of functioning of complex buildings by facilitating certain patterns of movement and/or impeding other patterns. In cities and suburban built environments, spatial configuration affects accessibilities and influences travel behavioural patterns, e.g. choosing walking and cycling for short trips instead of travelling by cars. As such, spatial configuration effectively influences the social, economic, and environmental functioning of cities and complex buildings, by conducting human movement patterns. In this research, graph theory is used to mathematically model spatial configurations in order to provide intuitive ways of studying and designing spatial arrangements for architects and urban designers. The methods and tools presented in this dissertation are applicable in: arranging spatial layouts based on configuration graphs, e.g. by using bubble diagrams to ensure certain spatial requirements and qualities in complex buildings; and analysing the potential effects of decisions on the likely spatial performance of buildings and on mobility patterns in built environments for systematic comparison of designs or plans, e.g. as to their aptitude for pedestrians and cyclists. The dissertation reports two parallel tracks of work on architectural and urban configurations. The core concept of the architectural configuration track is the ‘bubble diagram’ and the core concept of the urban configuration track is the ‘easiest paths’ for walking and cycling. Walking and cycling have been chosen as the foci of this theme as they involve active physical, cognitive, and social encounter of people with built environments, all of which are influenced by spatial configuration. The methodologies presented in this dissertation have been implemented in design toolkits and made publicly available as freeware applications

Proceedings of the Seventh International Conference Formal Approaches to South Slavic and Balkan languages

Proceedings of the Seventh International Conference Formal Approaches to South Slavic and Balkan Languages publishes 17 papers that were presented at the conference organised in Dubrovnik, Croatia, 4-6 Octobre 2010

Meaning versus Grammar

This volume investigates the complicated relationship between grammar, computation, and meaning in natural languages. It details conditions under which meaning-driven processing of natural language is feasible, discusses an operational and accessible implementation of the grammatical cycle for Dutch, and offers analyses of a number of further conjectures about constituency and entailment in natural language

Prolegomena to a Semantic Theory for Natural Languages Based on Recursive Artihmetic

In this dissertation, the possibility of employing a version of (primitive) recursive arith- metic to build the semantic representations of natural language sentences is explored. This idea derives from the fact that such a formal system differs under several respects from formalisms which have been traditionally employed in formal semantics, based on classical predicate logic. Specifically, in the case of recursive arithmetic, quantifiers are not primitive terms of the language, but they are defined as peculiar recursive functions; additionally, within it they cannot be defined in a way which corresponds to how they have traditionally been conceived, i.e. as “unbounded” quantifiers, whose domain is not necessarily finite. In recursive arithmetic, however, it is possible to convey something equivalent to general assertions, regarding any arbitrarily chosen individual, by using free variables; crucially, such variables do not establish relations of scope with other terms of the language, and their interpretation can to a large extent be assimilated to that of wide scope standard universal quantifiers. In the light of this, it is argued that several linguistic phenomena, attested in natural languages of different families, can be explained in an especially natural way by assuming that the lexical elements and syn- tactic structures involved are correlated with the presence of these free variables with generic value in the logical form of the sentence. In particular, generic indefinites, con- ditionals and habitual clauses are analyzed, in their interaction with the negation and, as for the first two, with quantified noun phrases; in connection with these aspects, the problem of the internal structure of negative indefinite is also addressed; finally, a pos- sible analysis of the Neg-Raising phenomenon in terms of generic variables is offered. Many of the proposals made here have already appeared in the literature, in Löbner (2000, 2013) and, moreover, in Goodstein (1951, 1957) and Hornstein (1984). Some apparent counterexamples to the theory outlined are explained by making appeal to an independently motivated treatment of embedded clauses. It is suggested that the analyzed phenomena, when collectively considered, confirm the validity of the initial project, letting one glimpse new potential scenarios for a fruitful exchange between the philosophy of mathematics and linguistic semantics

Balancing exploration and exploitation: task-targeted exploration for scientific decision-making

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September 2022.How do we collect observational data that reveal fundamental properties of scientific phenomena? This is a key challenge in modern scientific discovery. Scientific phenomena are complex—they have high-dimensional and continuous state, exhibit chaotic dynamics, and generate noisy sensor observations. Additionally, scientific experimentation often requires significant time, money, and human effort. In the face of these challenges, we propose to leverage autonomous decision-making to augment and accelerate human scientific discovery. Autonomous decision-making in scientific domains faces an important and classical challenge: balancing exploration and exploitation when making decisions under uncertainty. This thesis argues that efficient decision-making in real-world, scientific domains requires task-targeted exploration—exploration strategies that are tuned to a specific task. By quantifying the change in task performance due to exploratory actions, we enable decision-makers that can contend with highly uncertain real-world environments, performing exploration parsimoniously to improve task performance. The thesis presents three novel paradigms for task-targeted exploration that are motivated by and applied to real-world scientific problems. We first consider exploration in partially observable Markov decision processes (POMDPs) and present two novel planners that leverage task-driven information measures to balance exploration and exploitation. These planners drive robots in simulation and oceanographic field trials to robustly identify plume sources and track targets with stochastic dynamics. We next consider the exploration- exploitation trade-off in online learning paradigms, a robust alternative to POMDPs when the environment is adversarial or difficult to model. We present novel online learning algorithms that balance exploitative and exploratory plays optimally under real-world constraints, including delayed feedback, partial predictability, and short regret horizons. We use these algorithms to perform model selection for subseasonal temperature and precipitation forecasting, achieving state-of-the-art forecasting accuracy. The human scientific endeavor is poised to benefit from our emerging capacity to integrate observational data into the process of model development and validation. Realizing the full potential of these data requires autonomous decision-makers that can contend with the inherent uncertainty of real-world scientific domains. This thesis highlights the critical role that task-targeted exploration plays in efficient scientific decision-making and proposes three novel methods to achieve task-targeted exploration in real-world oceanographic and climate science applications.This material is based upon work supported by the NSF Graduate Research Fellowship Program and a Microsoft Research PhD Fellowship, as well as the Department of Energy / National Nuclear Security Administration under Award Number DE-NA0003921, the Office of Naval Research under Award Number N00014-17-1-2072, and DARPA under Award Number HR001120C0033