1,720,978 research outputs found
Clustering in Block Markov Chains
Get PDFThis paper considers cluster detection in Block Markov Chains (BMCs). These Markov chains are characterized by a block structure in their transition matrix. More precisely, the possible states are divided into a finite number of groups or clusters, such that states in the same cluster exhibit the same transition rates to other states. One observes a trajectory of the Markov chain, and the objective is to recover, from this observation only, the (initially unknown) clusters. In this paper we devise a clustering procedure that accurately, efficiently, and provably detects the clusters. We first derive a fundamental information-theoretical lower bound on the detection error rate satisfied under any clustering algorithm. This bound identifies the parameters of the BMC, and trajectory lengths, for which it is possible to accurately detect the clusters. We next develop two clustering algorithms that can together accurately recover the cluster structure from the shortest possible trajectories, whenever the parameters allow detection. These algorithms thus reach the fundamental detectability limit, and are optimal in that sense
Scaling Limits and Generic Bounds for Exploration Processes
Get PDFWe consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become blocked. Given an initial number of vertices N growing to infinity, we study statistical properties of the proportion of explored (active or blocked) nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the jamming constant, through a diffusion approximation for the exploration process which can be described as a unidimensional process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e., random sequential adsorption. As opposed to exploration processes on homogeneous random graphs, these do not allow for such a dimensional reduction. Instead we derive a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and we obtain generic bounds for the fluid limit and jamming constant: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, using coupling techinques, we give trajectorial interpretations of the generic bounds.Fil: Bermolen, Paola. Universidad de la Republica. Facultad de Ingeniería; UruguayFil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Sanders, Jaron. Eindhoven Technical University; Países Bajo
Markov Chains and Hitting Times for Error Accumulation in Quantum Circuits
No full textWe study a classical model for the accumulation of errors in multi-qubit quantum computations. By modeling the error process in a quantum computation using two coupled Markov chains, we are able to capture a weak form of time-dependency between errors in the past and future. By subsequently using techniques from the field of discrete probability theory, we calculate the probability that error quantities such as the fidelity and trace distance exceed a threshold analytically. The formulae cover fairly generic error distributions, cover multi-qubit scenarios, and are applicable to the randomized benchmarking protocol. To combat the numerical challenge that may occur when evaluating our expressions, we additionally provide an analytical bound on the error probabilities that is of lower numerical complexity. Besides this, we study a model describing continuous errors accumulating in a single qubit. Finally, taking inspiration from the field of operations research, we illustrate how our expressions can be used to decide how many gates one can apply before too many errors accumulate with high probability, and how one can lower the rate of error accumulation in existing circuits through simulated annealing.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Network Architectures and Service
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Reinforcement Learning in Block Markov Chains
No full textNowadays, reinforcement learning algorithms on Markov decision processes (MDPs) face computational issues when the state space is large. To reduce this state space of a MDP several state aggregation, or clustering, methodologies have been applied. Recently, a new clustering algorithm has been proposed that is able to cluster states from a single block Markov chain. A block Markov chain is a Markov chain with blocks in its transition matrix that correspond to clusters. Our aim was to investigate the possible combination of state aggregation in reinforcement learning on MDPs with clustering of states on a block Markov chain. First, we investigated the clustering algorithm and its properties to see its performance with different parameters and trajectory length. We compared the statistical properties of a pure Markov chain and the mixed Markov chain generated by a MDP. Afterwards, we verified the performance of the clustering algorithm on this mixed Markov chain. We proposed the BMC-MDP model that is able to model cluster based MDPs. We proposed C-PSRL, an algorithm, that consists of a single clustering step, on this newly introduced model. We compared its performance with a naïve approach and concluded that this new combined approach of clustering and MDP solving on a reduced space is a viable approach that reduces the computational complexity significantly. This research opened up the possibilities of more complex algorithms with, for example, multiple clustering steps. Moreover, if we can extend this clustering algorithm to clustering based on a state and action trajectory, this may results in an increased clustering performance and thereby enhance the performance of this general approach of optimizing on a cluster based MDP.Electrical Engineerin
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