<p>Switching networks are a common model for biological systems, especially</p><p>for genetic transcription networks. Stuart Kaufman originally proposed</p><p>the usefulness of the Boolean framework, but much of the dynamical </p><p>features there are not realizable in a continuous analogue. We introduce the notion</p><p>of braid-like dynamics as a bridge between Boolean and continuous dynamics and</p><p>study its importance in the local dynamics of ring and ring-like networks. We discuss</p><p>a near-theorem on the global dynamics of general feedback networks, and in the final</p><p>chapter study the main ideas of this thesis in models of a yeast cell transcription network.</p> / Dissertation

In models for networks of regulatory interactions in biological molecules, the sigmoid relationship between concentration of regulating bodies and the production rates they control has lead to the use of continuous time 'switching' ordinary differential equations (ODEs), sometimes referred to as Glass networks. These Glass networks are the result of a simplifying assumption that the switching behaviour occurs instantaneously at particular threshold values. Though this assumption produces highly tractable models, it also causes analytic difficulties in certain cases due to the discontinuities of the system, such as non-uniqueness. In this thesis we explore the use of 'ramp' functions as an alternative approximation to the sigmoid, which restores continuity to the ODE and removes the assumption of infinitely fast switching by linearly interpolating the focal point values used in a corresponding Glass network. A general framework for producing a ramp system from a certain Glass network is given. Solutions are explored in two dimensions, and then in higher dimensions under two different restrictions. Periodic behaviour is explored in both cases using mappings between threshold boundaries. Limitations in these methods are explored, and a general proof of the existence of periodic solutions in negative feedback loops is given. / Graduate

[non communiqué] / For the last three decades, the optical fiber has been a quite systematic response to dimensioning issues in the Internet. Originally restricted to long haul networks, the optical network has gradually descended the network hierarchy to discard the bottlenecks. In the 90's, metropolitan networks became optical. Today, optical fibers are deployed in access networks and reach the users. In a near future, besides wireless access and local area networks, all networks in the network hierarchy may be made of fibers, in order to support current services (HDTV) and the emergence of new applications (3D-TV newly commercialized in USA). The deployment of such greedy applications will initiate an upward upgrade. The first step may be the Metropolitan Area Networks (MANs), not only because of the traffic growth, but also because of the variety of served applications, each with a specific traffic profile. The current optical layer is of mitigated efficiency, dealing with unforeseen events. The lack of reactivity is mainly due to the slow switching devices: any on-line decision of the optical layer is delayed by the configuration of the. devices. When the optical network has been extended in the MANs, a lot of efforts has been deployed to improve the reactivity of the optical layer. The Optical Circuit Switching paradigm (OCS) has been improved but it ultimately relies on off-line configuration of the optical devices. Optical Burst Switching (OBS) can be viewed as a highly flexible evolution of OCS, that operates five order of magnitude faster. Within this 'architecture, the loss-free guaranty can be abandoned in order to improve the reactivity of the optical layer. Indeed, reliability and reactivity appear as antagonists properties and getting closer to either of them mitigates the other. This thesis aims at proposing a solution to achieve reliable transmission over a dynamic optical layer. Focusing on OBS networks, our objective is to solve the contention issue without mitigating the reactivity. After the consideration of contention avoidance mechanisms with routing constraints similar as in OCS networks, we investigate the reactive solutions that intend to solve the contentions. None of the available contention resolution scheme can ensure the 100% efficiency that leads to loss-free transmission. An attractive solution is the recourse to electrical buffering, but it is notoriously disregarded because (1) it may highly impact the delays and (2) loss can occur due to buffer overflows. The efficiency of translucent architectures thus highly depends on the buffer availability, that can be improved by reducing the time spent in the buffers and the contention rate. We show that traffic grooming can highly reduce the emission delay, and consequently the buffer occupancy. In a first architecture, traffic grooming is enabled by a translucent core node architecture, capable to re-aggregate incoming bursts. The re-aggregation is mandatory to "de-groom" the bursts in the core network (i.e., to demultiplex the content of a burst). On the one hand, the re-aggregation highly reduces the loss probability, but on the other hand, it absorbs the benefits of traffic grooming. Finally, dynamic access to re-aggregation for contention resolution, despite the significant reduction of the contention rate, dramatically impacts the end-to-end delay and the memory requirement. We thus propose a second architecture, called CAROBS, that exploits traffic grooming in the optical domain. This framework is fully dynamic and can be used jointly with our translucent architecture that performs re-aggregation. As the (de)grooming operations do not involve re-aggregation, the translucent module can be restricted to contention resolution. As a result, the volume of data submitted to re-aggregation is drastically reduced and loss-free transmission can be reached with the same reactivity, end-to-end delay and memory requirement as a native OBS network

Inference of regulatory relations in dynamical systems is a promising active research area. Recently, most of the investigations in this field have been stimulated by the researches in functional genomics. In this thesis, the inferential modeling problem for switching hybrid systems is studied. The hybrid systems refers to dynamical systems in which discrete and continuous variables regulate each other, in other words the jumps and flows are interrelated. In this study, piecewise linear approximations are used for modeling purposes and it is shown that piecewise linear models are capable of displaying the evolutionary characteristics of switching hybrid systems approxi- mately. For the mentioned systems, detection of switching instances and inference of locally linear parameters from empirical data provides a solid understanding about the system dynamics. Thus, the inference methodology is based on these issues. The primary difference of the inference algorithm is the idea of transforming the switch- ing detection problem into a jump detection problem by derivative estimation from discrete data. The jump detection problem has been studied extensively in signal processing literature. So, related techniques in the literature has been analyzed care- fully and suitable ones adopted in this thesis. The primary advantage of proposed method would be its robustness in switching detection and derivative estimation. The theoretical background of this robustness claim and the importance of robustness for real world applications are explained in detail.

A substantial increase in the number of internet users and the traffic volume bring new challenges for network router design. The current routers need to support higher link data rates and large number of line cards to accommodate the growth of the internet traffic, which necessitate an increase in physical space, power and memory use. Packet forwarding, which is one of the major tasks of a router, has been a performance bottleneck in internet infrastructure. In general, most of the packet forwarding algorithms are implemented in software. However, hardware based solutions has also been popular in recent years because of their high throughput performance. Besides throughput, memory efficiency, incremental/dynamic updates and power consumption are the basic performance challenges for packet forwarding architectures. Hardware-based packet forwarding engines for network routers can be categorized into two groups that are ternary content addressable memory (TCAM) based and dynamic/static random access memory (DRAM/SRAM) based solutions. TCAM-based architectures are simple and hence popular solutions for today&rsquo / s routers. However, they are expensive, power-hungry, and oer little adaptability to new addressing and routing protocols. On the other hand, SRAM has higher density, lower power consumption, and higher speed. The common data structure used in SRAM-based solutions for performing longest prefix matching (LPM) is some type of a tree. In these solutions, multiple memory accesses are required to find the longest matched prefix. Therefore, parallel and pipelining techniques are used to improve the throughput. This thesis studies TCAM and SRAM based parallel and pipelined architectures for high performance packet forwarding. We proposed to use a memory efficient disjoint prefix set algorithm on TCAM based parallel IP packet forwarding engine to improve its performance. As a fundamental contribution of this thesis, we designed an SRAM based parallel, intersecting and variable length multi-pipeline array structure (SAFIL) for trie-based internet protocol (IP) lookup. We also proposed a novel dual port SRAM based high throughput IP lookup engine (SAFILD) which is built upon SAFIL. As an alternative to traditional binary trie, we proposed a memory efficient data structure called compact clustered trie (CCT) for IP lookup. Furthermore, we developed a novel combined length-infix pipelined search (CLIPS) architecture for high performance IPv4/v6 lookup on FPGA. Finally, we designed a memory efficient clustered hierarchical search structure (CHSS) for packet classification. A linear pipelined SRAM-based architecture for CHSS which is implemented on FPGA is also proposed.