A Fast Scheduling Algorithm for WDM Optical Networks

Wavelength Division Multiplexing (WDM) is emerging as the most promising approach to exploit the huge bandwidth of optical fibre. This approach divides the optical spectrum into many different channels where each channel corresponds to a different wavelength. Single-hop WDM networks are attractive in local area environment where all the nodes can be connected to a single broadcast facility. In a single-hop WDM broadcast network, the transmitter must know when to transmit a packet and at which wavelength, while the receiver must know when to tune to the appropriate wavelength to receive the packet. This process requires some form of coordination. Many researches have focused on the scheduling algorithms that perform this kind of coordination. This thesis proposes a scheduling algorithm for the WDM broadcast networks. The algorithm employs a theory in graph, known as edge colouring of bipartite multigraph to produce the transmission schedule, which is free from collision due to the nature of the edge colouring. An optimal edge colouring of bipartite multi graph can be found in O(M log2 N) time, where M is number of packets selected for scheduling, and N is the number of the nodes. This time complexity can be improved to O(log3 N) by parallel processing using O(M) processors. Two variations of implementation of the scheduling algorithm have been proposed, namely the Variable Frame Size (VFS) and Limited Frame Size (LFS) schemes. These schemes use different criteria to select packets from the nodes for scheduling. The VFS scheme is simple, but supports only best effort transmissions. The LFS scheme ensures the frame size of the transmission schedule is bounded, thus enabling it to support bandwidth guarantee to the nodes up to a node's fair share of the network capacity. The LFS scheme is capable of supporting constant bit rate and unspecified bit rate service categories, analogous to the Asynchronous Transfer Mode (ATM) services. The results show that the LFS scheme performs better than the VFS scheme in terms of channel utilisation, packet loss probability and network throughput for all the simulated traffic patterns, especially at heavy loads. Besides, the LFS scheme respects any level of bandwidth guarantee, while the unused bandwidth can be used for best effort transmissions. The results also show that the VFS and LFS schemes are future-proof as they are able to capitalise on the increase in the number of wavelength channels

Lorentz-invariant, retrocausal, and deterministic hidden variables

We review several no-go theorems attributed to Gisin and Hardy, Conway and Kochen purporting the impossibility of Lorentz-invariant deterministic hidden-variable model for explaining quantum nonlocality. Those theorems claim that the only known solution to escape the conclusions is either to accept a preferred reference frame or to abandon the hidden-variable program altogether. Here we present a different alternative based on a foliation dependent framework adapted to deterministic hidden variables. We analyse the impact of such an approach on Bohmian mechanics and show that retrocausation (that is future influencing the past) necessarily comes out without time-loop paradox

Uniqueness of the gauge invariant action for cosmological perturbations

In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cubic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higss inflation.Comment: 27 page

The Cosmological Constant Problem and Re-interpretation of Time

We abandon the interpretation that time is a global parameter in quantum mechanics, replace it by a quantum dynamical variable playing the role of time. This operational re-interpretation of time provides a solution to the cosmological constant problem. The expectation value of the zero-point energy under the new time variable vanishes. The fluctuation of the vacuum energy as the leading contribution to the gravitational effect gives a correct order to the observed "dark energy". The "dark energy" as a mirage is always seen comparable with the matter energy density by an observer using the internal clock time. Conceptual consequences of the re-interpretation of time are also discussed.Comment: 9 pages, no figure; v3: improved discussion on remote simultaneity; v4: improved discussion on coincidence problem, reproduced Einstein theory of gravity from quantum reference frame, typos corrected, updated to the final version published in Nuclear Physics

Aspects of Galilean and Relativistic Particle Mechanics with Dirac's Constraints

Relevant physical models are described by singular Lagrangians, so that their Hamiltonian description is based on the Dirac theory of constraints. The qualitative aspects of this theory are now understood, in particular the role of the Shanmugadhasan canonical transformation in the determination of a canonical basis of Dirac's observables allowing the elimination of gauge degrees of freedom from the classical description of physical systems. This programme was initiated by Dirac for the electromagnetic field with charged fermions. Now Dirac's observables for Yang-Mills theory with fermions (whose typical application is QCD) have been found in suitable function spaces where the Gribov ambiguity is absent. Also the ones for the Abelian Higgs model are known and those for the $SU(2) \times U(1)$ electroweak theory with fermions are going to be found with the same method working for the Abelian case. The main task along these lines will now be the search of Dirac's observables for tetrad gravity in the case of asymptotically flat 3-manifolds. The philosophy behind this approach is ``first reduce, then quantize": this requires a global symplectic separation of the physical variables from the gauge ones so that the role of differential geometry applied to smooth field configurations is dominating, in contrast with the standard approach of ``first quantizing, then reducing", where, in the case of gauge field theory, the reduction process takes place on distributional field configurations, which dominate in quantum measures. This global separation has been accomplished till now, at least at a heuristic level, and one is going to have a classical (pseudoclassical for the fermion) variables basis for the physical description of the $SU(3)\times SU(2)\times U(1)$ standard model; instead, with tetrad gravity one expects toComment: Talk given at the Conference ``Theories of Fundamental Interactions", Maynooth (Ireland), May 1995. (LaTeX file

Explaining Individual Differences in Executive Functions Performance in Multilinguals: The Impact of Code-Switching and Alternating Between Multicultural Identity Styles

This study sheds new light on the relative impact of switching between languages and switching between cultures on Executive Functions (EFs) in bilinguals. Several studies have suggested that bilingualism has a measurable impact on executive functioning, presumably due to bilinguals’ constant practice in dealing with two languages, or two cultures. Yet, the evidence on the relative contribution of culture and bilingualism to EFs is not well understood, because disentangling language, culture and immigration status is very difficult. The novelty of our approach was to keep the language pair and immigration status constant, whilst the cultural identity of participants was systematically varied, and measured at the individual level (not just at group level). Two groups of Turkish–English bilinguals, all adult immigrants to the United Kingdom, took part in the study, but one group (n = 29) originated from mainland Turkey and the other (n = 28) from Cyprus. We found that the bilinguals experienced smaller Conflict Effects on a Flanker task measuring inhibition, by comparison with monolingual British participants (n = 30). The key variable explaining EF performance variance at the individual level turned out to be bilinguals’ Multicultural Identity Style. In particular those who indicated that they attempted to alternate between different British and Turkish (Cypriot) identity styles were found to have shorter RTs on incongruent trials of the Flanker task. The two multicultural identity variables, Alternating and Hybrid Identity Styles, together explained 32% in RTs over and above Education, Working Memory and Nonverbal reasoning (overall explained variance 49%). Thus, the data provide strong evidence for the impact of culture on EFs. We suggest that, as a result of their daily practice in recognizing cultural cues which highlight the need to switch to a different cultural frame, multicultural bilinguals develop a heightened context-sensitivity, and this gives them an advantage over monolinguals in a Flankers task. Our approach, which draws on models from cross-cultural psychology, bilingualism and executive functioning, illustrates the importance of theory building in which sociolinguistic and cultural variables are integrated into models of EFs