Power domains and iterated function systems

We introduce the notion of weakly hyperbolic iterated function system (IFS) on a compact metric space, which generalises that of hyperbolic IFS. Based on a domain-theoretic model, which uses the Plotkin power domain and the probabilistic power domain respectively, we prove the existence and uniqueness of the attractor of a weakly hyperbolic IFS and the invariant measure of a weakly hyperbolic IFS with probabilities, extending the classic results of Hutchinson for hyperbolic IFSs in this more general setting. We also present finite algorithms to obtain discrete and digitised approximations to the attractor and the invariant measure, extending the corresponding algorithms for hyperbolic IFSs. We then prove the existence and uniqueness of the invariant distribution of a weakly hyperbolic recurrent IFS and obtain an algorithm to generate the invariant distribution on the digitised screen. The generalised Riemann integral is used to provide a formula for the expected value of almost everywh..

The Kato Square Root Problem for Mixed Boundary Conditions

We consider the negative Laplacian subject to mixed boundary conditions on a bounded domain. We prove under very general geometric assumptions that slightly above the critical exponent $\frac{1}{2}$ its fractional power domains still coincide with suitable Sobolev spaces of optimal regularity. In combination with a reduction theorem recently obtained by the authors, this solves the Kato Square Root Problem for elliptic second order operators and systems in divergence form under the same geometric assumptions.Comment: Inconsistencies in Section 6 remove

A Recipe for State-and-Effect Triangles

In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an adjunction between state- and predicate-transformers. The current paper exploits a classical result in category theory, part of Jon Beck's monadicity theorem, to systematically construct such a state-and-effect triangle from an adjunction. The power of this construction is illustrated in many examples, covering many monads occurring in program semantics, including (probabilistic) power domains

Robust Pilot Decontamination Based on Joint Angle and Power Domain Discrimination

We address the problem of noise and interference corrupted channel estimation in massive MIMO systems. Interference, which originates from pilot reuse (or contamination), can in principle be discriminated on the basis of the distributions of path angles and amplitudes. In this paper we propose novel robust channel estimation algorithms exploiting path diversity in both angle and power domains, relying on a suitable combination of the spatial filtering and amplitude based projection. The proposed approaches are able to cope with a wide range of system and topology scenarios, including those where, unlike in previous works, interference channel may overlap with desired channels in terms of multipath angles of arrival or exceed them in terms of received power. In particular we establish analytically the conditions under which the proposed channel estimator is fully decontaminated. Simulation results confirm the overall system gains when using the new methods.Comment: 14 pages, 5 figures, accepted for publication in IEEE Transactions on Signal Processin

Asynchronous Circuit Stacking for Simplified Power Management

As digital integrated circuits (ICs) continue to increase in complexity, new challenges arise for designers. Complex ICs are often designed by incorporating multiple power domains therefore requiring multiple voltage converters to produce the corresponding supply voltages. These converters not only take substantial on-chip layout area and/or off-chip space, but also aggregate the power loss during the voltage conversions that must occur fast enough to maintain the necessary power supplies. This dissertation work presents an asynchronous Multi-Threshold NULL Convention Logic (MTNCL) “stacked” circuit architecture that alleviates this problem by reducing the number of voltage converters needed to supply the voltage the ICs operate at. By stacking multiple MTNCL circuits between power and ground, supplying a multiple of VDD to the entire stack and incorporating simple control mechanisms, the dynamic range fluctuation problem can be mitigated. A 130nm Bulk CMOS process and a 32nm Silicon-on-Insulator (SOI) CMOS process are used to evaluate the theoretical effect of stacking different circuitry while running different workloads. Post parasitic physical implementations are then carried out in the 32nm SOI process for demonstrating the feasibility and analyzing the advantages of the proposed MTNCL stacking architecture

Synthesis of application specific processor architectures for ultra-low energy consumption

In this paper we suggest that further energy savings can be achieved by a new approach to synthesis of embedded processor cores, where the architecture is tailored to the algorithms that the core executes. In the context of embedded processor synthesis, both single-core and many-core, the types of algorithms and demands on the execution efficiency are usually known at the chip design time. This knowledge can be utilised at the design stage to synthesise architectures optimised for energy consumption. Firstly, we present an overview of both traditional energy saving techniques and new developments in architectural approaches to energy-efficient processing. Secondly, we propose a picoMIPS architecture that serves as an architectural template for energy-efficient synthesis. As a case study, we show how the picoMIPS architecture can be tailored to an energy efficient execution of the DCT algorithm