Notes on the Poisson point process
... is sometimes called a purely or completely random process [18]. Despite its wide use as a stochastic model of phenomena representable as points, the inherent nature of the process implies that it does not adequately describe phenomena in which there is sufficiently strong interaction between the poi ...
... is sometimes called a purely or completely random process [18]. Despite its wide use as a stochastic model of phenomena representable as points, the inherent nature of the process implies that it does not adequately describe phenomena in which there is sufficiently strong interaction between the poi ...
Notes on the Poisson point process
... is sometimes called a purely or completely random process [18]. Despite its wide use as a stochastic model of phenomena representable as points, the inherent nature of the process implies that it does not adequately describe phenomena in which there is sufficiently strong interaction between the poi ...
... is sometimes called a purely or completely random process [18]. Despite its wide use as a stochastic model of phenomena representable as points, the inherent nature of the process implies that it does not adequately describe phenomena in which there is sufficiently strong interaction between the poi ...
legal institutions and informal networks
... Fearon and Laitin, 1996), we do not model these cultural effects. Nor does our model directly incorporate the common argument that cooperative networks are sustained through social norms that change people’s preferences through an evolutionary or socialization process such that individuals prefer co ...
... Fearon and Laitin, 1996), we do not model these cultural effects. Nor does our model directly incorporate the common argument that cooperative networks are sustained through social norms that change people’s preferences through an evolutionary or socialization process such that individuals prefer co ...
Continuous Homophily and Clustering in Random Networks
... cases these networks are very large and remain unknown for an analysis, typically random networks are used as an approximation. This constitutes a challenge to design the random network formation process in a way to ensure it complies with the observed stylized facts. Since the seminal work of Erdo ...
... cases these networks are very large and remain unknown for an analysis, typically random networks are used as an approximation. This constitutes a challenge to design the random network formation process in a way to ensure it complies with the observed stylized facts. Since the seminal work of Erdo ...
hku m01
... Remark 6. Poisson process provides rather good approximation for modeling many random processes such as the arrival of customers and calls. From the proposition above, a process is Poisson (with coefficient λ) if and only if the inter-arrival times (the lengths of time between successive customer arr ...
... Remark 6. Poisson process provides rather good approximation for modeling many random processes such as the arrival of customers and calls. From the proposition above, a process is Poisson (with coefficient λ) if and only if the inter-arrival times (the lengths of time between successive customer arr ...
Stochastic processes I: Asymptotic behaviour and symmetries 1)
... Our concern here will be to present a phenomenological theory of macroscopic systems whith are not necessarily in a thermodynamic equilibrium. For the description of systems in terms of a finite set of degrees of freedom which do not behave in a deterministic way but display statistical fluctuations ...
... Our concern here will be to present a phenomenological theory of macroscopic systems whith are not necessarily in a thermodynamic equilibrium. For the description of systems in terms of a finite set of degrees of freedom which do not behave in a deterministic way but display statistical fluctuations ...
paper
... different in both technique and results. Our goal is not to derive network capacity regions, but rather to develop equivalence relationships between the capacity regions of distinct networks. In other words, we wish to show that any collection of connections is feasible on one network if and only if ...
... different in both technique and results. Our goal is not to derive network capacity regions, but rather to develop equivalence relationships between the capacity regions of distinct networks. In other words, we wish to show that any collection of connections is feasible on one network if and only if ...
2 Graphical Models in a Nutshell
... same Markov network, along with the node and edge potentials. We use P 1, P 2, P 3, and P 4 for shorthand. In this case, all of the node and edge potentials are the same, but this is not a requirement. The node potentials show that the patients are much more likely to be uninfected. The edge potenti ...
... same Markov network, along with the node and edge potentials. We use P 1, P 2, P 3, and P 4 for shorthand. In this case, all of the node and edge potentials are the same, but this is not a requirement. The node potentials show that the patients are much more likely to be uninfected. The edge potenti ...
Statistical Issues in the Analysis of Neuronal Data
... an update to the early work of Perkel et al. (1967a,b). The new field of computational neuroscience uses detailed biophysical models and artificial neural networks to study emergent behavior of neural systems and the way neural systems represent and transmit information (e.g., Dayan and Abbott 2001) ...
... an update to the early work of Perkel et al. (1967a,b). The new field of computational neuroscience uses detailed biophysical models and artificial neural networks to study emergent behavior of neural systems and the way neural systems represent and transmit information (e.g., Dayan and Abbott 2001) ...
Menu-Dependent Stochastic Feasibility
... (Theorem 3.3). We also characterize a model where π has limited support in Appendix C of the Supplemental Material. We now present the main result. Theorem 3.1. A random choice rule satisfies ASI, TSI, ESI, and IFO if and only if it is an RCCSR P,π . Moreover, both and π are unique, that is, for ...
... (Theorem 3.3). We also characterize a model where π has limited support in Appendix C of the Supplemental Material. We now present the main result. Theorem 3.1. A random choice rule satisfies ASI, TSI, ESI, and IFO if and only if it is an RCCSR P,π . Moreover, both and π are unique, that is, for ...
Innovation, growth and aggregate volatility from a
... for flexible estimation procedures via conditional (or posterior) distributions. For our purposes, one of the main advantages of this approach is represented by the fact that it yields intuitive and coherent prediction mechanisms for modeling unseen species, categories, genes but also types of econo ...
... for flexible estimation procedures via conditional (or posterior) distributions. For our purposes, one of the main advantages of this approach is represented by the fact that it yields intuitive and coherent prediction mechanisms for modeling unseen species, categories, genes but also types of econo ...
Mathematical Finance in discrete time
... We recall here basic notions from probability theory which we will need for modeling financial markets. ...
... We recall here basic notions from probability theory which we will need for modeling financial markets. ...
arXiv:math/0610716v2 [math.PR] 16 Feb 2007
... the axes, and under rotations through multiples of π/2. Thirdly, well separated regions are asymptotically independent: more precisely, let ρ > 0 and η > 0 be constants. Given ε > 0, if s is large enough, then for R1 and R2 two ρs by s rectangles separated by a distance of at least ηs, and E1 and E2 ...
... the axes, and under rotations through multiples of π/2. Thirdly, well separated regions are asymptotically independent: more precisely, let ρ > 0 and η > 0 be constants. Given ε > 0, if s is large enough, then for R1 and R2 two ρs by s rectangles separated by a distance of at least ηs, and E1 and E2 ...
Stochastic Processes
... that fn −→ f µ-a.e. pointwise as n → +∞. If there exists a function g ≥ 0 in Lq (µ) such that |fn | ≤ g, for every n ∈ N, then f ∈ Lq (µ) and the convergence takes place also in Lq (µ). Now we state the theorem of B. Levi on monotone convergence. 1.A.4 Theorem. Let (fn )n∈N be a monotone sequence of ...
... that fn −→ f µ-a.e. pointwise as n → +∞. If there exists a function g ≥ 0 in Lq (µ) such that |fn | ≤ g, for every n ∈ N, then f ∈ Lq (µ) and the convergence takes place also in Lq (µ). Now we state the theorem of B. Levi on monotone convergence. 1.A.4 Theorem. Let (fn )n∈N be a monotone sequence of ...
Dynamic Generation of Scenario Trees
... It has been shown in Pflug and Pichler [20] that an appropriate distance concept for stochastic processes and trees is given by the nested distance (see Definition 18 below). The relevant theorem for multistage stochastic optimization (cited as Theorem 19 below) is extended and simplified for the p ...
... It has been shown in Pflug and Pichler [20] that an appropriate distance concept for stochastic processes and trees is given by the nested distance (see Definition 18 below). The relevant theorem for multistage stochastic optimization (cited as Theorem 19 below) is extended and simplified for the p ...
Journal of Neuroscience Methods Estimation of neuronal firing rates
... recordings (LeadPoint-Medtronic, Minneapolis), each approximately 1 s in length, from inside both the right and left STNs of ten right-handed subjects (four female). It should be noted that we specifically analyse relatively short lengths of MER data to emphasize the suitability of our approach to re ...
... recordings (LeadPoint-Medtronic, Minneapolis), each approximately 1 s in length, from inside both the right and left STNs of ten right-handed subjects (four female). It should be noted that we specifically analyse relatively short lengths of MER data to emphasize the suitability of our approach to re ...
[pdf]
... Since a Markov logic network is not (necessarily) specific to concrete domain elements but is instead designed to be applicable to arbitrary domains over the classes of objects that it models, MLNs should satisfy the generality requirement made above. However, with the current set of concepts in pla ...
... Since a Markov logic network is not (necessarily) specific to concrete domain elements but is instead designed to be applicable to arbitrary domains over the classes of objects that it models, MLNs should satisfy the generality requirement made above. However, with the current set of concepts in pla ...
Community Detection on Evolving Graphs
... becomes better in the case of skewed distributions. For example, if we have n1/3 clusters, and the associated probabilities are αi ∼ 1/i2 , the first strategy incorrectly classifies O(n1/3 ) nodes in each step (in expectation), compared to only O(log2 n) nodes misclassified by the second strategy. F ...
... becomes better in the case of skewed distributions. For example, if we have n1/3 clusters, and the associated probabilities are αi ∼ 1/i2 , the first strategy incorrectly classifies O(n1/3 ) nodes in each step (in expectation), compared to only O(log2 n) nodes misclassified by the second strategy. F ...
Choice and the Weak Axiom of Stochastic Revealed Preference
... properties. We proceed to show that our domain restriction is also necessary for RG to imply WASRP, when the universal set is finite. Lastly, we provide a necessary and sufficient domain restriction under which RG and WASRP are equivalent, when the universal set is finite and stochastic choice funct ...
... properties. We proceed to show that our domain restriction is also necessary for RG to imply WASRP, when the universal set is finite. Lastly, we provide a necessary and sufficient domain restriction under which RG and WASRP are equivalent, when the universal set is finite and stochastic choice funct ...
Doob: Half a century on - Imperial College London
... Daniell- Kolmogorov theorem (as in the Grundbegriffe) – essentially the existence theorem for a stochastic process, given the minimal raw material of an appropriately consistent set of finite-dimensional distributions. The main emphasis is on conditioning (Kolmogorov’s treatment of conditioning in ...
... Daniell- Kolmogorov theorem (as in the Grundbegriffe) – essentially the existence theorem for a stochastic process, given the minimal raw material of an appropriately consistent set of finite-dimensional distributions. The main emphasis is on conditioning (Kolmogorov’s treatment of conditioning in ...
Sophie Hautphenne â Research Fellow in Applied Probability
... [16] S. Hautphenne, G. Krings, J-C. Delvenne and V. D. Blondel. Sensitivity analysis of a branching process evolving on a network with application in epidemiology. Journal of complex networks, doi:10.1093/comnet/cnv001, 2015. [15] S. Hautphenne, Y. Kerner, Y. Nazarathy and P. Taylor. The intercept t ...
... [16] S. Hautphenne, G. Krings, J-C. Delvenne and V. D. Blondel. Sensitivity analysis of a branching process evolving on a network with application in epidemiology. Journal of complex networks, doi:10.1093/comnet/cnv001, 2015. [15] S. Hautphenne, Y. Kerner, Y. Nazarathy and P. Taylor. The intercept t ...
Module 5 - University of Pittsburgh
... Consider then a vertex v that has at least two neighbors, which we will denote i and j. Being neighbors of Consider v, i and j are node both at the ends has of edges and hence the numberi and of other u that at from ...
... Consider then a vertex v that has at least two neighbors, which we will denote i and j. Being neighbors of Consider v, i and j are node both at the ends has of edges and hence the numberi and of other u that at from ...
Bayesian networks - Center for Computational Biology and
... technology simultaneously measures only 12 molecules in individual cells, although there are many more molecules involved in a typical signaling response). Bayesian networks have been used for automatic reconstruction of causal signaling network models from data derived from individual primary human ...
... technology simultaneously measures only 12 molecules in individual cells, although there are many more molecules involved in a typical signaling response). Bayesian networks have been used for automatic reconstruction of causal signaling network models from data derived from individual primary human ...
Stochastic geometry models of wireless networks
In mathematics and telecommunications, stochastic geometry models of wireless networks refer to mathematical models based on stochastic geometry that are designed to represent aspects of wireless networks. The related research consists of analyzing these models with the aim of better understanding wireless communication networks in order to predict and control various network performance metrics. The models require using techniques from stochastic geometry and related fields including point processes, spatial statistics, geometric probability, percolation theory, as well as methods from more general mathematical disciplines such as geometry, probability theory, stochastic processes, queueing theory, information theory, and Fourier analysis.In the early 1960s a pioneering stochastic geometry model was developed to study wireless networks. This model is considered to be the origin of continuum percolation. Network models based on geometric probability were later proposed and used in the late 1970s and continued throughout the 1980s for examining packet radio networks. Later their use increased significantly for studying a number of wireless network technologies including mobile ad hoc networks, sensor networks, vehicular ad hoc networks, cognitive radio networks and several types of cellular networks, such as heterogeneous cellular networks. Key performance and quality of service quantities are often based on concepts from information theory such as the signal-to-interference-plus-noise ratio, which forms the mathematical basis for defining network connectivity and coverage.The principal idea underlying the research of these stochastic geometry models, also known as random spatial models, is that it is best to assume that the locations of nodes or the network structure and the aforementioned quantities are random in nature due to the size and unpredictability of users in wireless networks. The use of stochastic geometry can then allow for the derivation of closed-form or semi-closed-form expressions for these quantities without resorting to simulation methods or (possibly intractable or inaccurate) deterministic models.