Partitioning de Bruijn Graphs into Fixed-Length Cycles for Robot Identification and Tracking

We propose a new camera-based method of robot identification, tracking and orientation estimation. The system utilises coloured lights mounted in a circle around each robot to create unique colour sequences that are observed by a camera. The number of robots that can be uniquely identified is limited by the number of colours available, $q$, the number of lights on each robot, $k$, and the number of consecutive lights the camera can see, $\ell$. For a given set of parameters, we would like to maximise the number of robots that we can use. We model this as a combinatorial problem and show that it is equivalent to finding the maximum number of disjoint $k$-cycles in the de Bruijn graph $\text{dB}(q,\ell)$. We provide several existence results that give the maximum number of cycles in $\text{dB}(q,\ell)$ in various cases. For example, we give an optimal solution when $k=q^{\ell-1}$. Another construction yields many cycles in larger de Bruijn graphs using cycles from smaller de Bruijn graphs: if $\text{dB}(q,\ell)$ can be partitioned into $k$-cycles, then $\text{dB}(q,\ell)$ can be partitioned into $tk$-cycles for any divisor $t$ of $k$. The methods used are based on finite field algebra and the combinatorics of words.Comment: 16 pages, 4 figures. Accepted for publication in Discrete Applied Mathematic

Investigation of demographic factors in construction employees' safety perceptions

This study focused on the effects of these demographic factors on construction employees’ safety perceptions. It first initiated a theoretical framework illustrating the impacts of demographic factors (i.e., education level, gender, and age) on employee’s perceptions towards pre-defined site hazards as well as their general safety perception. Then site questionnaire survey approach was adopted in nine construction jobsites in southeastern China followed by statistical analysis. The study revealed that construction employees’ education level, although not affecting their perceptions towards safety hazards/accidents, could create differences in other general safety perceptions between management staff and workers. Gender differences were found in safety perceptions of hazard/accident scenes and general safety perceptions, indicating that gender issue in safety perceptions applied consistently crossing different industries. Employees between 37 and 46 years old tended to underestimate safety risks from commonly encountered hazards, suggesting the needs of continued safety refreshers for employees in the middle of their career. This study contributed to the body of knowledge in safety perceptions by investigating the effect of three major subgroup or demographic factors, including education level, gender, and age, which had not been sufficiently addressed in construction safety subculture or sub-climate

Observed and Physical Properties of Core-Collapse Supernovae

I use photometry and spectroscopy data for 24 Type II plateau supernovae to examine their observed and physical properties. This dataset shows that these objects encompass a wide range of ~5 mag in their plateau luminosities, their expansion velocities vary by x5, and the nickel masses produced in these explosions go from 0.0016 to 0.26 Mo. From a subset of 16 objects I find that the explosion energies vary between 0.6x and 5.5x10^51 ergs, the ejected masses encompass the range 14-56 Mo, and the progenitors' radii go from 80 to 600 Ro. Despite this great diversity several regularities emerge, which reveal that there is a continuum in the properties of these objects from the faint, low-energy, nickel-poor SNe 1997D and 1999br, to the bright, high-energy, nickel-rich SN 1992am. This study provides evidence that more massive progenitors produce more energetic explosions, thus suggesting that the outcome of the core collapse is somewhat determined by the envelope mass. I find also that supernovae with greater energies produce more nickel. Similar relationships appear to hold for Type Ib/c supernovae, which suggests that both Type II and Type Ib/c supernovae share the same core physics. When the whole sample of core collapse objects is considered, there is a continous distribution of energies below 8x10^51 ergs. Far above in energy scale and nickel production lies the extreme hypernova 1998bw, the only supernova firmly associated to a GRB.Comment: 25 pages, 7 figures, accepted for Part 1 of Astrophysical Journa

Challenges and resilience: managers' perceptions of firm performance following M&As

We study M&As, resilience and performance, identifying links between managers’ perceptions of performance and resilience, using trans-national organisational-level survey evidence (N=3613) and follow up semi-structured in-depth interviews with managers involved in M&As and demerger. Drawing on the resilience and M&A literature, we identify reasons why employees in acquired firms may be less resilient in coping with the resultant changes than those of the acquirer and why this will negatively impact perceptions of performance. We explore the causes and consequences of variations in resilience and performance within firms that acquire others, and in those that have been demerged. As anticipated, we find that although managers in acquired firms tended to report worse performance than those in acquiring firms, both tended to be more positive than firms that had not taken part in an M&A at all. We draw out implications for theory and practice

Continuous and discontinuous phase transitions and partial synchronization in stochastic three-state oscillators

We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical evidence that the continuity of the transition depends on the coupling coefficients and, in some nonuniform populations, on the degree of quenched disorder. Hence, in a relatively simple setting this class of models exhibits the qualitative behaviors characteristic of a variety of considerably more complicated models. In addition, we study the microscopic basis of synchronization above threshold and detail the counterintuitive subtleties relating measurements of time averaged frequencies and mean field oscillations. Most notably, we observe a state of suprathreshold partial synchronization in which time-averaged frequency measurements from individual oscillators do not correspond to the frequency of macroscopic oscillations observed in the population

Freezing Points Of Aqueous Alcohols: Free Energy Of Interaction Of The CHOH, CH₂, CONH And C[double bond]C Functional Groups In Dilute Aqueous Solutions

The freezing temperatures of dilute aqueous solutions of methanol, ethanol, 2-propanol, butanol, t-butanol, cyclohexanol and ethylene glycol were measured over the concentration range 0.1 to 1 mol kg–1. Osmotic coefficients at 0°C were calculated. The limiting pairwise interaction coefficients of the alcohols, plus a variety of polyhydroxy compounds and carbohydrates, were calculated at 25°C from the available data and then correlated using the additivity principle of Savage and Wood. This correlation approximates effective free energies of CH2 and CHOH group interactions with themselves and with each other. Literature data were used to estimate interactions between CONH and C[double bond]C groups. The CONH—CONH interaction appears to be large, consistent with a strong stabilizing effect of these on native protein structures. The CH2…CH2 interaction also indicates attractive forces between these groups. The present model for the hydrophobic interaction is most appropriate for small molecular interactions whereas previous treatments are best for situations involving site binding. The CHOH…CHOH and CH2…CONH interactions are small, while the CHOH…CH2 free energy of interaction is positive, due either to volume exclusion or net repulsive forces. The entropy change associated with the CH2…CH2 interaction is large and positive as expected and is not completely compensated by a corresponding enthalpy change. The entropy change associated with the CONH…CONH interaction indicates that few degrees of freedom are involved, which is consistent with the formation of a strong hydrogen bond. The correlation can be used to estimate thermodynamic properties of dilute non-electrolyte solutions and can also predict the effect of solutes on the solubility of solids and gases

A science mapping approach based review of construction safety research

This study adopted a three-step holistic review approach consisting of bibliometric review, scientometric analysis, and in-depth discussion to gain a deeper understanding of the research development in construction safety. Focusing on a total of 513 journal articles published in Scopus, the influential journals, keywords, scholars, and articles in the domain of construction safety were analyzed

The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.