Tree-like Processes Research Articles

Dendritic Cells and Vaccines

Note: Dr. Steinman received the prestigious 2007 Albert Lasker Award for Basic Medical Research for the discovery of dendritic cells. The award committee called him “a scientific sleuth, who without cloak and dagger, uncovered the intelligence-gathering component of our immune system—a monumental achievement in the 200-year history of immunology.” Dr. Steinman came to Baylor on September 20, 2007, as part of the celebration of the tenth anniversary of the Baylor Institute for Immunology Research (Figure ​(Figure11). We were honored to welcome him and appreciate his willingness to publish his well-received presentation in Proceedings. Figure 1 Ralph M. Steinman, MD, with Jacques Banchereau, PhD, director of the Baylor Institute for Immunology Research. —Michael a. e. Ramsay, MD, associate editor and president of Baylor Research Institute Immunology plays an important role in many clinical conditions. In some instances—such as infectious diseases and cancer—the goal is to improve the immune response to the pathogen or challenge; in other instances—such as transplantation, autoimmunity, and allergy—the goal is to reduce the specific immune response. Already, immunology is providing valuable therapies, mainly in the form of monoclonal antibodies. Anti–tumor necrosis factor (TNF) is being used to treat arthritis and other inflammatory diseases, and anti-CD20 is being used to treat B cell lymphoma. However, the T cell limb of the immune response also needs to be harnessed in a disease- or antigen-specific manner in medicine. This opportunity in immunology and medicine is significant because of the way T cells are formed. The immune system is blessed with a superb repertoire of clones (Figure ​(Figure22). Each clone has a specific receptor for antigen, and within that repertoire are clones specific for microbes, tumors, self, the environment, and so forth—many of the relevant antigens to disease. Thus, the repertoire provides the potential for antigen-specific therapies and vaccines, which will mount a broad-based but specific response to the relevant pathogen, in contrast to cyclosporine, for example, which is a general immunosuppressant. Figure 2 Three elemental R's of T cell biology: repertoire, recognition, response. Reprinted with permission from Nature Medicine (1). One of the main goals in human immunology research is to establish the principles to manipulate these clones in a patient, so that they will expand and carry out the function that is appropriate to a successful therapy. At the Rockefeller University and the Baylor Institute for Immunology Research, one of the main approaches is to try to harness the biology of dendritic cells, which use their tree-like processes or dendrites to constantly probe their environment (Figure ​(Figure33). Figure 3 Dendritic cells probing the environment in mouse lymphoid tissue. Photomicrograph courtesy of Dr. Juliana Idoyaga; reprinted with permission from Nature Medicine (1).

Dynamic exploration of networks: from general principles to the traceroute process

Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on a class of tree-like processes, such as those used to explore the Internet's topology. A general theory based on mean-field arguments is proposed, both for single-source and multiple-source cases, and applied to the specific example of the traceroute exploration of networks. Our results provide a qualitative improvement in the understanding of dynamical sampling and of the interplay between dynamics and topology in large networks like the Internet.

Analyzing priority queues with 3 classes using tree-like processes

In this paper we demonstrate how tree-like processes can be used to analyze a general class of priority queues with three service classes, creating a new methodology to study priority queues. The key result is that the operation of a 3-class priority queue can be mimicked by means of an alternate system that is composed of a single stack and queue. The evolution of this alternate system is reduced to a tree-like Markov process, the solution of which is realized through matrix analytic methods. The main performance measures, i.e., the queue length distributions and loss rates, are obtained from the steady state of the tree-like process through a censoring argument. The strength of our approach is demonstrated via a series of numerical examples.

Transient analysis of tree-Like processes and its application to random access systems

A new methodology to assess transient performance measures of tree-like processes is proposed by introducing the concept of tree-like processes with marked time epochs. As opposed to the standard tree-like process, such a process marks part of the time epochs by following a set of Markovian rules. Our interest lies in obtaining the system state at the n -th marked time epoch as well as the mean time at which this n -th marking occurs. The methodology transforms the transient problem into a stationary one by applying a discrete Erlangization and constructing a reset Markov chain. A fast algorithm, with limited memory usage, that exploits the block structure of the reset Markov chain is developed and is based, among others, on Sylvester matrix equations and fast Fourier transforms. The theory of tree-like processes generalizes the well-known paradigm of Quasi-Birth-Death Markov chains and has various applications. We demonstrate our approach on the celebrated Capetanakis-Tsybakov-Mikhailov (CTM) random access protocol yielding new insights on its initial behavior both in normal and overload conditions.

Linking priority queues and tree-like processes

This paper links the analysis of a general class of priority queues with three service classes with tree-like processes. This is realized by demonstrating that the operation of a 3-class priority queue can be mimicked by means of an alternate system that is composed of a single stack and queue. Some insights on how to reduce the evolution of this alternate system to a tree-like process are provided, allowing an efficient solution of the priority system through matrix analytic methods.

Architectures of Biological Complexity

Three features contribute to the complexity of an entity: number of parts, their order, and their iteration. Many functional biological entities are complex when measured by those attributes, and although they are produced in tree-like architectures, the organizational structures that permit them to function are in the form of hierarchies. Natural hierarchies can be thought of as organizing structures that are emergent properties of complex functional entities, and which are transformed from trees by process networks. For example, hierarchies are observed in the architecture of metazoan bodies (the somatic hierarchy) and in the biotic structure of ecogeographic units (the ecological hierarchy). As the metazoan developmental genome is quite complex and has been evolved through tree-like processes, it must harbor at least one hierarchy, which is most clearly indicated in the developmental processes that create the somatic hierarchy. For multicellular organisms, the processes that serve to transform trees of gene expression events into a somatic hierarchy have produced complicated signaling networks whose histories can probably be recovered in general outline.

On the Complexity of Deciding Behavioural Equivalences and Preorders. A Survey

This paper gives an overview of the computational complexity of all the equivalences in the linear/branching time hierarchy [vG90a] and the preorders<br />in the corresponding hierarchy of preorders. We consider finite state or regular processes as well as infinite-state BPA [BK84b] processes. <br />A distinction, which turns out to be important in the finite-state processes, is that of simulation-like equivalences/preorders vs. trace-like equivalences<br />and preorders. Here we survey various known complexity results for these relations. For regular processes, all simulation-like equivalences and preorders are decidable in polynomial time whereas all trace-like equivalences and preorders are PSPACE-Complete. We also consider interesting special<br />classes of regular processes such as deterministic, determinate, unary, locally unary, and tree-like processes and survey the known complexity results in<br />these special cases. For infinite-state processes the results are quite different. For the class of context-free processes or BPA processes any preorder or equivalence beyond bisimulation is undecidable but bisimulation equivalence is polynomial time<br />decidable for normed BPA processes and is known to be elementarily decidable in the general case. For the class of BPP processes, all preorders and equivalences apart from bisimilarity are undecidable. However, bisimilarity<br />is decidable in this case and is known to be decidable in polynomial time for normed BPP processes.