A diagrammatic approach to networks of spans and relations

In this thesis we exhibit nondeterministic semantics for various classes of circuits. Motivated initially by quantum circuits, we also give nondeterministic semantics for circuits for classical mechanical systems and Boolean algebra. More formally, we interpret these classes of circuits in terms of categories of spans or relations: in less categorical terms these are equivalent to matrices over the natural numbers or the Boolean semiring. In the relational picture, we characterize circuits in terms of which inputs and outputs are jointly possible; and in the spans picture, how often inputs and outputs are jointly possible. Specifically, we first show that the class of circuits generated by the Toffoli gate as well the states |0⟩, |1⟩, √2|+⟩ and their adjoints is characterized in terms of spans of finite sets. We also give a complete axiomatization for these circuits. With this semantics in mind, we discuss the connection to partial and reversible computation. Shifting to the phase-space picture we also characterize circuits in terms of how they relate abstract positions and momenta. We show how this gives a unifying relational semantics for certain classes circuits for classical mechanical systems, as well as for stabilizer quantum circuit

Quality of service optimization of multimedia traffic in mobile networks

Mobile communication systems have continued to evolve beyond the currently deployed Third Generation (3G) systems with the main goal of providing higher capacity. Systems beyond 3G are expected to cater for a wide variety of services such as speech, data, image transmission, video, as well as multimedia services consisting of a combination of these. With the air interface being the bottleneck in mobile networks, recent enhancing technologies such as the High Speed Downlink Packet Access (HSDPA), incorporate major changes to the radio access segment of 3G Universal Mobile Telecommunications System (UMTS). HSDPA introduces new features such as fast link adaptation mechanisms, fast packet scheduling, and physical layer retransmissions in the base stations, necessitating buffering of data at the air interface which presents a bottleneck to end-to-end communication. Hence, in order to provide end-to-end Quality of Service (QoS) guarantees to multimedia services in wireless networks such as HSDPA, efficient buffer management schemes are required at the air interface. The main objective of this thesis is to propose and evaluate solutions that will address the QoS optimization of multimedia traffic at the radio link interface of HSDPA systems. In the thesis, a novel queuing system known as the Time-Space Priority (TSP) scheme is proposed for multimedia traffic QoS control. TSP provides customized preferential treatment to the constituent flows in the multimedia traffic to suit their diverse QoS requirements. With TSP queuing, the real-time component of the multimedia traffic, being delay sensitive and loss tolerant, is given transmission priority; while the non-real-time component, being loss sensitive and delay tolerant, enjoys space priority. Hence, based on the TSP queuing paradigm, new buffer managementalgorithms are designed for joint QoS control of the diverse components in a multimedia session of the same HSDPA user. In the thesis, a TSP based buffer management algorithm known as the Enhanced Time Space Priority (E-TSP) is proposed for HSDPA. E-TSP incorporates flow control mechanisms to mitigate congestion in the air interface buffer of a user with multimedia session comprising real-time and non-real-time flows. Thus, E-TSP is designed to provide efficient network and radio resource utilization to improve end-to-end multimedia traffic performance. In order to allow real-time optimization of the QoS control between the real-time and non-real-time flows of the HSDPA multimedia session, another TSP based buffer management algorithm known as the Dynamic Time Space Priority (D-TSP) is proposed. D-TSP incorporates dynamic priority switching between the real-time and non-real-time flows. D-TSP is designed to allow optimum QoS trade-off between the flows whilst still guaranteeing the stringent real-time component’s QoS requirements. The thesis presents results of extensive performance studies undertaken via analytical modelling and dynamic network-level HSDPA simulations demonstrating the effectiveness of the proposed TSP queuing system and the TSP based buffer management schemes

Blow-ups and normal bundles in connective and nonconnective derived geometries

This work presents a generalization of derived blow-ups and of the derived deformation to the normal bundle from derived algebraic geometry to any geometric context. The latter is our proposed globalization of a derived algebraic context, itself a generalization of the theory of simplicial commutative rings. One key difference between a geometric context and ordinary derived algebraic geometry is that the coordinate ring of an affine object in the former is not necessarily connective. When constructing generalized blow-ups, this not only turns out to be remarkably convenient, but also leads to a wider existence result. Indeed, we show that the derived Rees algebra and the derived blow-up exist for any affine morphism of stacks in a given geometric context. However, in general the derived Rees algebra will no longer be connective, hence in general the derived blow-up will not live in the connective part of the theory. Unsurprisingly, this can be solved by restricting the input to closed immersions. The proof of the latter statement uses a derived deformation to the normal bundle in any given geometric context, which is also of independent interest. Besides the geometric context which extends algebraic geometry, the second main example of a geometric context will be an extension of analytic geometry. The latter is a recent construction, and includes many different flavors of analytic geometry, such as complex analytic geometry, non-archimedean rigid analytic geometry and analytic geometry over the integers. The present work thus provides derived blow-ups and a derived deformation to the normal bundle in all of these, which is expected to have many applications.Comment: 50 page

A criterion for existence of right-induced model structures

Suppose that $F: \mathcal{N} \to \mathcal{M}$ is a functor whose target is a Quillen model category. We give a succinct sufficient condition for the existence of the right-induced model category structure on $\mathcal{N}$ in the case when $F$ admits both adjoints. We give several examples, including change-of-rings, operad-like structures, and anti-involutive structures on infinity categories. For the last of these, we explore anti-involutive structures for several different models of $(\infty, 1)$-categories, and show that known Quillen equivalences between base model categories lift to equivalences

Stabilizer Reduction for Derived Stacks and Applications to Sheaf-Theoretic Invariants

We construct a canonical stabilizer reduction $\widetilde{X}$ for any derived $1$-algebraic stack $X$ over $\mathbb{C}$ as a sequence of derived Kirwan blow-ups, under mild natural conditions that include the existence of a good moduli space for the classical truncation $X_{\mathrm{cl}}$. Our construction naturally generalizes Kirwan's classical partial desingularization algorithm to the context of derived algebraic geometry. We prove that $\widetilde{X}$ is a natural derived enhancement of the intrinsic stabilizer reduction constructed by Kiem, Li and the third author. Moreover, if $X$ is $(-1)$-shifted symplectic, we show that the semi-perfect and almost perfect obstruction theory and their induced virtual fundamental cycle and virtual structure sheaf of $\widetilde{X}_{\mathrm{cl}}$, constructed by the same authors, are naturally induced by $\widetilde{X}$ and its derived tangent complex. As a corollary, we give a fully derived perspective on generalized Donaldson-Thomas invariants of Calabi-Yau threefolds and define new generalized Vafa-Witten invariants for surfaces via Kirwan blow-ups.Comment: 68 pages. Comments welcome

Minimizing the communication overhead of iterative scheduling algorithms for input-queued switches

Communication overhead should be minimized when designing iterative scheduling algorithms for input-queued packet switches. In general, the overall communication overhead is a function of the number of iterations required per time slot (M) and the data bits exchanged in an input-output pair per iteration (B). In this paper, we aim at maximizing switch throughput while minimizing communication overhead. We first propose a single-iteration scheduling algorithm called Highest Rank First (HRF). In HRF, the highest priority is given to the preferred input-output pair calculated in each local port at a RR (Round Robin) order. Only when the preferred VOQ(i,j) is empty, input i sends a request with a rank number r to each output. The request from a longer VOQ carries a smaller r. Higher scheduling priority is given to the request with a smaller r. To further cut down its communication overhead to 1 bit per request, we design HRF with Request Compression (HRF/RC). The basic idea is that we transmit a single bit code in request phase. Then r can be decoded at output ports from the current and historical codes received. The overall communication overhead for HRF/RC becomes 2 bits only, i.e. 1 bit in request phase and 1 bit in grant phase. We show that HRF/RC renders a much lower hardware cost than multi-iteration algorithms and a single-iteration algorithm π-RGA [11]. Compared with other iterative algorithms with the same communication overhead (i.e. SRR [10] and 1-iteration iSLIP [6]), simulation results show that HRF/RC always produces the best delay-throughput performance. © 2011 IEEE.published_or_final_versionProceedings of the IEEE Global Telecommunications Conference (GLOBECOM 2011), Houston, TX, USA, 5-9 December 201

Traffic management framework for supporting integrated services in cross-path switch.

Lau Tsz-ming.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 57-[61]).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Integrated Services Architecture --- p.2Chapter 1.2 --- Cross-path Switch --- p.4Chapter 1.2.1 --- Path Switching --- p.5Chapter 1.3 --- Organization of Thesis --- p.9Chapter 2 --- Module Architecture --- p.10Chapter 2.1 --- Introduction --- p.10Chapter 2.2 --- Notable Features --- p.11Chapter 3 --- Connection Admission Control and Resource Allocation --- p.14Chapter 3.1 --- Introduction --- p.14Chapter 3.2 --- Connection Admission Control --- p.15Chapter 3.2.1 --- Guaranteed Service --- p.15Chapter 3.2.2 --- Controlled-Load Service --- p.18Chapter 3.3 --- Resource Allocation --- p.27Chapter 4 --- Resource Management --- p.31Chapter 4.1 --- Introduction --- p.31Chapter 4.2 --- Scheduling Algorithm --- p.32Chapter 4.2.1 --- Input and Output Module --- p.32Chapter 4.2.2 --- Central Module --- p.34Chapter 4.3 --- Buffer Management --- p.39Chapter 4.3.1 --- Buffer Partitioning --- p.40Chapter 4.3.2 --- Dicard Policy --- p.40Chapter 5 --- Design Issue of Cross-path Switch --- p.43Chapter 5.1 --- Introduction --- p.43Chapter 5.2 --- Stability Condition --- p.44Chapter 5.3 --- Supplementary Admission Control Scheme --- p.46Chapter 5.4 --- Simulation --- p.50Chapter 6 --- Conclusion --- p.55Bibliography --- p.5