Simulating systematic bias in attributed social networks and its effect on rankings of minority nodes

Network analysis provides powerful tools to learn about a variety of social systems. However, most analyses implicitly assume that the considered relational data is error-free, and reliable and accurately reflects the system to be analysed. Especially if the network consists of multiple groups (e.g., genders, races), this assumption conflicts with a range of systematic biases, measurement errors and other inaccuracies that are well documented in the literature. To investigate the effects of such errors we introduce a framework for simulating systematic bias in attributed networks. Our framework enables us to model erroneous edge observations that are driven by external node attributes or errors arising from the (hidden) network structure itself. We exemplify how systematic inaccuracies distort conclusions drawn from network analyses on the task of minority representations in degree-based rankings. By analysing synthetic and real networks with varying homophily levels and group sizes, we find that the effect of introducing systematic edge errors depends on both the type of edge error and the level of homophily in the system: in heterophilic networks, minority representations in rankings are very sensitive to the type of systematic edge error. In contrast, in homophilic networks we find that minorities are at a disadvantage regardless of the type of error present. We thus conclude that the implications of systematic bias in edge data depend on an interplay between network topology and type of systematic error. This emphasises the need for an error model framework as developed here, which provides a first step towards studying the effects of systematic edge-uncertainty for various network analysis tasks.

Finite Element Method Analysis Applied to the Study of a Corner Joint in Reinforced Concrete Structures

The principal objective for this work was to extend the field of application of FEM to space frame beam-column connections under static loading and with lateral displacements. A four-storey building was modelled under static load condition. Horizontal and vertical structural elements were designed according to Eurocode 2. In order to understand the behavior of the external node made by under column, two beam and upper column, two models using correct boundary condition and nonlinear behavior of materials have been done using Abaqus Software The analysis was performed on an interior and an exterior joint models each in two conditions: unconfined and confined joint varying the distributions of number of stirrups for the beam reinforcement and the column reinforcement .A sup structural model to submit to numerical analysis have been performed, the Concrete Damage Plasticity model (CDPM) has been chosen for fit the nonlinear behavior for the concrete and the elastoplastic model has been adopted for the nonlinear behavior for the reinforcement (stirrups, longitudinal and vertical bars). The models were then verified against already existing and validated analytical results and results of experiments conducted on specimens.

Bayesian Testing for Exogenous Partition Structures in Stochastic Block Models

Network data often exhibit block structures characterized by clusters of nodes with similar patterns of edge formation. When such relational data are complemented by additional information on exogenous node partitions, these sources of knowledge are typically included in the model to supervise the cluster assignment mechanism or to improve inference on edge probabilities. Although these solutions are routinely implemented, there is a lack of formal approaches to test if a given external node partition is in line with the endogenous clustering structure encoding stochastic equivalence patterns among the nodes in the network. To fill this gap, we develop a formal Bayesian testing procedure which relies on the calculation of the Bayes factor between a stochastic block model with known grouping structure defined by the exogenous node partition and an infinite relational model that allows the endogenous clustering configurations to be unknown, random and fully revealed by the block–connectivity patterns in the network. A simple Markov chain Monte Carlo method for computing the Bayes factor and quantifying uncertainty in the endogenous groups is proposed. This strategy is evaluated in simulations, and in applications studying brain networks of Alzheimer’s patients.

Integrated Thermal Management in System-on-Package Devices

Thanks to the System-on-Package technology (SoP) the integration of different elements into a single package was enabled. However, from the thermal point of view the heat removal path in modern packaging technologies (FCBGA) goes through several layers of thermal interface material (TIM) that together with the package material create a relatively high thermal resistance which may lead to elevated chip temperature which causes functional error or other malfunctions. In our concept, we overcome this problem by creating integrated microfluidic channel based heat sink structures that can be used for cooling the high heat dissipation semiconductor devices (e.g.: processors, high power transistor or concentrated solar cells). These microchannel cooling assemblies can be integrated into the backside of the substrate of the semiconductor devices or into the system assemblies in SoP technology. In addition to the realization of the novel CMOS compatible microscale cooling device we have developed precise and valid measurement methodology, simulation cases studies and a unique compact model that can be added to numerical simulators as an external node. In this paper the achievements of a larger research are summarized as it required the cooperation of several experts in their fields to fulfil the goal of creating a state-of-the-art demonstrator. Thanks to the System-on-Package technology (SoP) the integration of different elements into a single package was enabled. However, from the thermal point of view the heat removal path in modern packaging technologies (FCBGA) goes through several layers of thermal interface material (TIM) that together with the package material create a relatively high thermal resistance which may lead to elevated chip temperature which causes functional error or other malfunctions. In our concept, we overcome this problem by creating integrated microfluidic channel based heat sink structures that can be used for cooling the high heat dissipation semiconductor devices (e.g.: processors, high power transistor or concentrated solar cells). These microchannel cooling assemblies can be integrated into the backside of the substrate of the semiconductor devices or into the system assemblies in SoP technology. In addition to the realization of the novel CMOS compatible microscale cooling device we have developed precise and valid measurement methodology, simulation cases studies and a unique compact model that can be added to numerical simulators as an external node. In this paper the achievements of a larger research are summarized as it required the cooperation of several experts in their fields to fulfil the goal of creating a state-of-the-art demonstrator.

A Note on Naturally Embedded Ternary Trees

In this note we consider ternary trees naturally embedded in the plane in a deterministic way. The root has position zero, or in other words label zero, and the three children of a node with position $j\in\mathbb{Z}$ have positions $j-1$, $j$, and $j+1$. We derive the generating function of embedded ternary trees where all internal nodes have labels less than or equal to $j$, with $j\in\mathbb{N}$. Furthermore, we study the generating function of the number of ternary trees of size $n$ with a given number of internal nodes with label $j$. Moreover, we discuss generalizations of this counting problem to several labels at the same time. We also study a refinement of the depth of the external node of rank $s$, with $0\le s\le 2n$, by keeping track of the left, center, and right steps on the unique path from the root to the external node. The $2n+1$ external nodes of a ternary tree are ranked from the left to the right according to an inorder traversal of the tree. Finally, we discuss generalizations of the considered enumeration problems to embedded $d$-ary trees.