Borel Cantelli Lemmas and Extreme Value Theory for Geometric Lorenz Models

We establish dynamical Borel-Cantelli lemmas for nested balls and rectangles centered at generic points in the setting of geometric Lorenz maps. We also establish extreme value statistics for observations maximized at generic points for geometric Lorenz maps and the associated flow

The reducibility of optimal 1-planar graphs with respect to the lexicographic product

A graph is called 1-planar if it can be drawn on the plane (or on the sphere) such that each edge is crossed at most once. A 1-planar graph $G$ is called optimal if it satisfies $|E(G)| = 4|V(G)|-8$. If $G$ and $H$ are graphs, then the lexicographic product $G\circ H$ has vertex set the Cartesian product $V(G)\times V(H)$ and edge set $\{(g_1,h_1) (g_2,h_2): g_1 g_2 \in E(G),\,\, \text{or}\,\, g_1=g_2 \,\, \text{and}\,\, h_1 h_2 \in E(H)\}$. A graph is called reducible if it can be expressed as the lexicographic product of two smaller non-trivial graphs. In this paper, we prove that an optimal 1-planar graph $G$ is reducible if and only if $G$ is isomorphic to the complete multipartite graph $K_{2,2,2,2}$. As a corollary, we prove that every reducible 1-planar graph with $n$ vertices has at most $4n-9$ edges for $n=6$ or $n\ge 9$. We also prove that this bound is tight for infinitely many values of $n$. Additionally, we give two necessary conditions for a graph $G\circ 2K_1$ to be 1-planar.Comment: 23 pages, 14 fugure

On the sizes of generalized cactus graphs

A cactus is a connected graph in which each edge is contained in at most one cycle. We generalize the concept of cactus graphs, i.e., a $k$-cactus is a connected graph in which each edge is contained in at most $k$ cycles where $k\ge 1$. It is well known that every cactus with $n$ vertices has at most $\lfloor\frac{3}{2}(n-1) \rfloor$ edges. Inspired by it, we attempt to establish analogous upper bounds for general $k$-cactus graphs. In this paper, we first characterize $k$-cactus graphs for $2\le k\le 4$ based on the block decompositions. Subsequently, we give tight upper bounds on their sizes. Moreover, the corresponding extremal graphs are also characterized. However, the case of $k\ge 5$ remains open. For the case of 2-connectedness, the range of $k$ is expanded to all positive integers in our research. We prove that every $2$-connected $k ~(\ge 1)$-cactus graphs with $n$ vertices has at most $n+k-1$ edges, and the bound is tight if $n \ge k + 2$. But, for $n < k+1$, determining best bounds remains a mystery except for some small values of $k$.Comment: 14 pages, 2 figure

Distributed resilient filtering of large-scale systems with channel scheduling

summary:This paper addresses the distributed resilient filtering for discrete-time large-scale systems (LSSs) with energy constraints, where their information are collected by sensor networks with a same topology structure. As a typical model of information physics systems, LSSs have an inherent merit of modeling wide area power systems, automation processes and so forth. In this paper, two kinds of channels are employed to implement the information transmission in order to extend the service time of sensor nodes powered by energy-limited batteries. Specifically, the one has the merit of high reliability by sacrificing energy cost and the other reduces the energy cost but could result in packet loss. Furthermore, a communication scheduling matrix is introduced to govern the information transmission in these two kind of channels. In this scenario, a novel distributed filter is designed by fusing the compensated neighboring estimation. Then, two matrix-valued functions are derived to obtain the bounds of the covariance matrices of one-step prediction errors and the filtering errors. In what follows, the desired gain matrices are analytically designed to minimize the provided bounds with the help of the gradient-based approach and the mathematical induction. Furthermore, the effect on filtering performance from packet loss is profoundly discussed and it is claimed that the filtering performance becomes better when the probability of packet loss decreases. Finally, a simulation example on wide area power systems is exploited to check the usefulness of the designed distributed filter

Designing a Unity Plugin to Predict Expected Affect in Games Using Biophilia

Video games can generate different emotional states and affective reactions, but it can sometimes be difficult for a game’s visual designer to predict the emotional response a player might experience when designing a game or game scene. In this thesis, I conducted a study to collect emotional responses to video game images. I then used that data to both confirm past research that suggests images can be used to predict affect and to build a model for predicting emotion that is specific to games. I built both a linear regression model and three neural network models to predict affective response and found that the neural net that leveraged ResNet-50 was most effective. I then incorporated that model into a Unity plug-in so that designers can use it to predict affect of players in real time

Towards conflict resolution and collaborative consensus-making: a participatory approach to architecture design in the Nottingham Natural History Museum, Wollaton Hall

Public engagement in museum design has been widely discussed and practiced. Public engagement not only inspires the participants’ interests and creativity, but also significantly increases the communication between the museum and participants. To date, however, most museum engagement projects have only focused on the exhibition design, while very few projects try to discuss public participation in the architecture design of museum. Therefore, this thesis sets out to find the most appropriate way that members of the public can participate in the architecture design of a museum. To answer this question, the thesis firstly reviews the history of museums, which explains that the purposes of museums have been extended from collection and preservation to exhibition, education and communication. What is more important, public participation in museum exhibition has become a new form of communication that remarkably improves the visitors’ experience. However, there is no doubt that the design of the museum building also plays a vital role in communicating with the local residents. The relationship between the museum building and society is intimate. The focus of the thesis then shifts to the theories of participatory architecture design that normally consists of architects, museum staff and members of the public. The professionals and laypeople normally have quite different knowledge and experience of architecture design. Therefore, a typical difficulty in processing the participatory architecture design is judging and structuring the different ideas. More specifically, one of the key issues of this thesis is how to deal with the power dominance and conflicts in participation that exists in this area. Following this issue, the thesis deduces the relationship between control and communication. On the one hand, the participation should minimise the control that exists in order to offer an open atmosphere for communication; on the other hand, communication should take place under a form/type of control that restricts the powerful or talkative participants from dominating any discussion. Furthermore, the conflict-resolving and collaborative consensus-making activities are two further essential aspects in participation. By comparing many different participation methods, Idea Rating Sheets (IRSs) and Consensus Mapping (CM) are considered as the two most appropriate methods in the architecture design of the museum. Idea Rating Sheets (IRSs) were created by Jason Diceman who is an expert on facilitation and public participation. Diceman has been the Senior Public Consultation Coordinator for the City of Toronto since 2010. Consensus Mapping (CM) is created by Stuart L. Hart, professor emeritus in the Johnson School of Management, Cornell University. He is one of the world's top authorities on the implications of environment and poverty for business strategy. Therefore, the main research question of this thesis is; “What is the performance of IRSs (Idea Rating Sheets) and CM (Consensus Mapping) in resolving conflicts and reaching collaborative consensus in the participatory architecture design of the museum?” It is difficult to describe the performance generally, so the thesis divides the main question into eight sub-questions. Regarding the eight sub-questions, a mixed methods research approach has been adopted: questionnaires, interviews and observations. Meanwhile, there are two pilot studies: 1) the testing of IRSs performance in judgment-making; and 2) the testing of questionnaires and interviews. Based on the two pilot studies, the author set up a participation workshop, specifically using the IRSs and CM in the architecture design of Nottingham Natural History Museum, Wollaton Hall. The workshop consists of Phase One (Group A) and Phase Two (Group B). The two phases have slightly different features in order to test the performance of IRSs and CM in different situations. Each group consists of an architect, a member of the museum staff, several local residents, a facilitator and an observer. Although this thesis mainly studies the participatory architecture design, the participants in the workshop actually discussed both architecture and exhibition design. By analysing the large amount of data collected, it can be argued that: 1) IRSs quantitatively and qualitatively support the production of options and judgments; 2) IRSs benefit the equal chance of expression, but the facilitator should also ask the participants individually for their responses; and 3) IRSs encourage the participants to express in-depth ideas and transfer any conflicts that emerge to achieve consensus. In addition to these points, the thesis also discussed the advantages and disadvantages of using the workshop and mixed research methods in the participation study. The conclusion of this thesis not only offers practical suggestions for participatory architecture design, but also informs potential future research topics