Heinrich Mann

Weisstein, Ulrich

doi:10.1515/9783111714394

Cited by 28 publications

(59 citation statements)

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“…The more general description of this concept is characterizing the relationship between system state and system trajectory, the basis of the study of Dynamical Systems [16] – that is, a system that evolves in time according to some rules in which future states evolve from the current state. In dynamical systems theory, an attractor is a state or set of states to which certain states tend to evolve [17]. A basin of attraction is the region of system state space under the influence of a given attractor as it affects given trajectories passing through these points (think analogously of gravitational wells in astrophysics).…”

Section: 0 Resultsmentioning

confidence: 99%

Sepsis reconsidered: Identifying novel metrics for behavioral landscape characterization with a high-performance computing implementation of an agent-based model

Cockrell

2017

Journal of Theoretical Biology

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Objectives Sepsis affects nearly 1 million people in the United States per year, has a mortality rate of 28–50% and requires more than $20 billion a year in hospital costs. Over a quarter century of research has not yielded a single reliable diagnostic test or a directed therapeutic agent for sepsis. Central to this insufficiency is the fact that sepsis remains a clinical/physiological diagnosis representing a multitude of molecularly heterogeneous pathological trajectories. Advances in computational capabilities offered by High Performance Computing (HPC) platforms call for an evolution in the investigation of sepsis to attempt to define the boundaries of traditional research (bench, clinical and computational) through the use of computational proxy models. We present a novel investigatory and analytical approach, derived from how HPC resources and simulation are used in the physical sciences, to identify the epistemic boundary conditions of the study of clinical sepsis via the use of a proxy agent-based model of systemic inflammation. Design Current predictive models for sepsis use correlative methods that are limited by patient heterogeneity and data sparseness. We address this issue by using an HPC version of a system-level validated agent-based model of sepsis, the Innate Immune Response ABM (IIRBM), as a proxy system in order to identify boundary conditions for the possible behavioral space for sepsis. We then apply advanced analysis derived from the study of Random Dynamical Systems (RDS) to identify novel means for characterizing system behavior and providing insight into the tractability of traditional investigatory methods. Results The behavior space of the IIRABM was examined by simulating over 70 million sepsis patients for up to 90 days in a sweep across the following parameters: cardio-respiratory-metabolic resilience; microbial invasiveness; microbial toxigenesis; and degree of nosocomial exposure. In addition to using established methods for describing parameter space, we developed two novel methods for characterizing the behavior of a RDS: Probabilistic Basins of Attraction (PBoA) and Stochastic Trajectory Analysis (STA). Computationally generated behavioral landscapes demonstrated attractor structures around stochastic regions of behavior that could be described in a complementary fashion through use of PBoA and STA. The stochasticity of the boundaries of the attractors highlights the challenge for correlative attempts to characterize and classify clinical sepsis. Conclusions HPC simulations of models like the IIRABM can be used to generate approximations of the behavior space of sepsis to both establish “boundaries of futility” with respect to existing investigatory approaches and apply system engineering principles to investigate the general dynamic properties of sepsis to provide a pathway for developing control strategies. The issues that bedevil the study and treatment of sepsis, namely clinical data sparseness and inadequate experimental sampling of system behavior space, are funda...

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Section: 0 Resultsmentioning

confidence: 99%

Sepsis reconsidered: Identifying novel metrics for behavioral landscape characterization with a high-performance computing implementation of an agent-based model

Cockrell

2017

Journal of Theoretical Biology

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“…According to Weisstein [12], a sample is the subset of a population that can be extracted by applying a process to select the elements, on a random basis or using another criterion. The purpose of a sample is to provide suffi cient data to investigate the properties of a population from which it was extracted.…”

Section: Modeling the Attack Environmentmentioning

confidence: 99%

“…The limits of the integration considered in equation (12) are complex numbers that represent initial and fi nal points that lie on the circumference g k . Although the initial point is coincident with the fi nal point of the complex plane, the numbers that represent these points are different.…”

Section: Determining the Ip Addressmentioning

confidence: 99%

An innovative approach to identify the IP address in denial‐of‐service (DoS) attacks based on Cauchy's integral theorem

Viana¹,

Rios²,

Andrade³

et al. 2008

Int J Network Mgmt

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Denial-of-service (DoS) and distributed denial-of-service (DDoS) are two of the most severe attacks against computer networks, especially the Internet. Despite its destructive effect, planning these attacks is a feasible task. Given that most attackers usually spoof the source address in packet headers, countermeasures can be based on two steps. First of all, some information from the attack space of the offender must be gathered. Fortunately, packets that reach a victim carry important data that can be acquired by means of a data collection process. One possibility is to use the probabilistic packet marking (PPM) approach for data acquisition. Once this is achieved, the next step consists of reconstructing the attack path, which can be carried out by several methods available in the literature. However, none of them provides a precise solution. In this paper, a new theoretical tracking model for the identifi cation of DoS attackers is presented. The model unites the PPM approach and the concept of winding number, derived from the well-known Cauchy's integral theorem. The winding number is a hydraulic analogy of the amount of attacking packets growing from a router. A suitable transformation allows seeing the packet traffi c, in the attack environment, as a fl uid fl ux in the space of complex variables. The method of solving the tracking problem and identifying the sources of attack presents an additional motivation: the use of continuous techniques when approaching a problem that occurs in a discrete environment. Such association will contribute to the development of further solutions possibly more robust than the one dealt with here. This paper shows that the new model can correctly identify the IP address of the router from which the attack comes by using an integral equation derived from the winding number expression. A1 A2 A3 R5 R6 R7 R3 R4 R2 R1 V Figure 1. Topology of the DoS attack environment AN INNOVATIVE APPROACH TO IDENTIFY THE IP ADDRESS IN DoS ATTACKS 341The goal of the injective function Φ is to associate each router R k , of set A, to a complex number of the form z k = x k + i.y k , in U. The elements that constitute the real, R (z k ) = x k , and imaginary, S (z k ) = y k , parts of the complex number z k correspond to Cartesian coordinates. These coordinates can be obtained, for instance, by means of instruments that detect the geographic global positioning (e.g., GPS receptors).On the other hand, once each point in the virtual space corresponds to a router that is represented by an IP address, the injective function Φ : A → U determines actually the (univocal) association of a pair of Cartesian coordinates. In order to fi nd a practical meaning for such an association, it is necessary to represent the injective function Φ by means of some mathematical expression. In the next section, an expression for Φ is presented, among others that could be considered for this task. DEFINITION OF THE FUNCTION Φ342 M. M. VIANA ET AL.a modifi cation on the protocol. Moreover, care must be taken regarding spoo...

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“…This procedure solves the problem for the Platonic solids, but it does not work for other more general meshes. However, the construction has the following property [17] that can be observed in Fig. 4 for the case of the icosahedron and the dodecahedron: for each edge e = {v 1 , v 2 , f 1 , f 2 } connecting two vertices and two faces, the segments joining the corresponding vertex positions and face positions intersect at their midpoints; i.e.,…”

Section: The Barycenter Dual Meshmentioning

confidence: 99%

“…In Section 4 we show that the dual vertex positions of the Platonic solids [17] circumscribed by a common sphere can also be defined as the solution of a least-squares problem with a quadratic energy function linking primal and dual vertex positions, and that this energy function is well defined for any manifold polygonal mesh without boundary. In Section 5 we derive explicit expressions for the new resampling dual vertex positions as linear functions of the primal vertex positions.…”

Section: Introductionmentioning

confidence: 99%

Dual Mesh Resampling

Taubin

2002

Graphical Models

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Heinrich Mann

Cited by 28 publications

References 0 publications

Sepsis reconsidered: Identifying novel metrics for behavioral landscape characterization with a high-performance computing implementation of an agent-based model

Sepsis reconsidered: Identifying novel metrics for behavioral landscape characterization with a high-performance computing implementation of an agent-based model

An innovative approach to identify the IP address in denial‐of‐service (DoS) attacks based on Cauchy's integral theorem

Dual Mesh Resampling

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