Extremal properties of flood-filling games

The problem of determining the number of "flooding operations" required to make a given coloured graph monochromatic in the one-player combinatorial game Flood-It has been studied extensively from an algorithmic point of view, but basic questions about the maximum number of moves that might be required in the worst case remain unanswered. We begin a systematic investigation of such questions, with the goal of determining, for a given graph, the maximum number of moves that may be required, taken over all possible colourings. We give several upper and lower bounds on this quantity for arbitrary graphs and show that all of the bounds are tight for trees; we also investigate how much the upper bounds can be improved if we restrict our attention to graphs with higher edge-density.Comment: Final version, accepted to DMTC

Gravity and the Quantum: Are they Reconcilable?

General relativity and quantum mechanics are conflicting theories. The seeds of discord are the fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal in the sense that a particle does not follow one trajectory, but infinitely many trajectories, each one with a different probability. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction, while torsion in teleparallel gravity acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principles. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics.Comment: 15 pages, 2 figures. Talk presented at the conference "Quantum Theory: Reconsideration of Foundations-3", June 6-11, 2005, Vaxjo University, Vaxjo, Swede

Gravitation without the equivalence principle

In the general relativistic description of gravitation, geometry replaces the concept of force. This is possible because of the universal character of free fall, and would break down in its absence. On the other hand, the teleparallel version of general relativity is a gauge theory for the translation group and, as such, describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction. Relying on this analogy it is shown that, although the geometric description of general relativity necessarily requires the existence of the equivalence principle, the teleparallel gauge approach remains a consistent theory for gravitation in its absence.Comment: Latex, 11 pages, no figures. Minor presentation changes. Version to appear in Gen. Rel. Grav. (2004

Doing without the Equivalence Principle

In Einstein's general relativity, geometry replaces the concept of force in the description of the gravitation interaction. Such an approach rests on the universality of free-fall--the weak equivalence principle--and would break down without it. On the other hand, the teleparallel version of general relativity, a gauge theory for the translation group, describes the gravitational interaction by a force similar to the Lorentz force of electromagnetism, a non-universal interaction. It is shown that, similarly to the Maxwell's description of electromagnetism, the teleparallel gauge approach provides a consistent theory for gravitation even in the absence of the weak equivalence principle.Comment: 7 pages, no figures. Talk presented at the "Tenth Marcel Grossmann Meeting", July 20 to 26, 2003, Rio de Janeiro, Brazil; to be published in the Proceedings (World Scientific, Singapore, 2005

Measuring Asymmetry and Persistence in Conditional Volatility in Real Output: Evidence from Three East Asian Tigers Using a Multivariate GARCH approach

We search for evidence of conditional volatility in the quarterly real GDP growth rates of three East Asian tigers: Singapore, Hong Kong and Taiwan. The widely accepted exponential GARCH-type model is used to capture the existence of asymmetric volatility and the potential structural break points in the volatility. We find evidence of asymmetry and persistence in the volatility of GDP growth rates. It is noted that the identified structural breakpoints of volatility correspond reasonably well to the historical economic and political events in these economies. Policy implications are discussed.East Asia, Real Output, GARCH, structural changes, asymmetric volatility

Use of Self Online

This study explores and documents the experiences and life changes of women who belong to the fastest-growing racial-ethnic group. Between 2000 and 2019, the Asian population in America grew by 81 percent (Budiman & Ruiz, 2021). Asian American women account for 19 percent of all immigrants between 2010 and 2015 (Neilsen, 2017). Just under 40 percent of Asian-American women identify themselves as entrepreneurs, which is more than any other group of women in the United States (Neilsen, 2017). This study presents the results of qualitative research that examines whether, and if so, how Hmong American women digital entrepreneurs embody the use of self (UoS) in their work. In-depth narrative inquiry is selected as the research methodology to explore Hmong women digital entrepreneurs’ stories of self-inquiry and personal growth. To elicit conversation, semi-structured open-ended interviews were conducted with five study participants. Participant story elements were compiled into fuller narratives coded for select elements within the stories and analyzed for themes across all of the stories. The research draws on two theoretical foundations to examine both data collection and data analysis. The theories include the over-arching constructivist perspective known as symbolic interactionism and feminist standpoint theory. The philosophy that one’s comprehension of reality occurs with reflexive engagement upon life experience through interaction with others is used to guide this research study (Bazeley, 2021). C. Wright Mills (1959) refers to this as “the sociological imagination” (p. 5), which is the ability to comprehend one’s own lived experience and situate it temporally and contextually. Standpoint theory, says 2 that knowledge develops from and is determined by social position, addresses the underlying epistemological issues with normative models and structures that do not describe the experiences of women (Sorell & Montgomery, 2001). This perspective sheds light on larger issues such as voice, belonging, discourse, power, and issues central to female development. The findings of this research reveal four broad themes that provide insight into similarities and differences in participant stories. The four themes that emerged from the data analysis include passion, connection, authenticity, and creative process. The participants in this study support previous findings that suggest there is an interconnectedness between participants’ identities, behavior, and stories. The construction of self online for these five women is not only an expression of their identity but also the embodiment of the best version of themselves. Furthermore, three main themes emerged as participants discussed how they engaged in self-inquiry and personal growth including critical self-reflection, outsider and well-being. As such, this study expands the research on use of self by studying Hmong American women, which is an understudied population and taking the research into the understudied context of digital media

Bringing Together Gravity and the Quanta

Due to its underlying gauge structure, teleparallel gravity achieves a separation between inertial and gravitational effects. It can, in consequence, describe the isolated gravitational interaction without resorting to the equivalence principle, and is able to provide a tensorial definition for the energy-momentum density of the gravitational field. Considering the conceptual conflict between the local equivalence principle and the nonlocal uncertainty principle, the replacement of general relativity by its teleparallel equivalent can be considered an important step towards a prospective reconciliation between gravitation and quantum mechanics.Comment: 9 pages. Contribution to the proceedings of the Albert Einstein Century International Conference, Paris, 18-22 July, 200

Very low loss reactively ion etched Tellurium Dioxide planar rib waveguides for linear and non-linear optics

We report on the fabrication and optical properties of the first very low loss nonlinear Tellurite planar rib waveguides ever demonstrated. A new reactive ion etch process based on Hydrogen as the active species was developed to accomplish the low propagation losses. Optical losses below ~0.05dB/cm in most of the NIR spectrum and ~0.10dB/cm at 1550nm have been achieved - the lowest ever reported by more than an order of magnitude and clearly suitable for planar integrated devices. We demonstrate strong spectral broadening of 0.6ps pulses in waveguides fabricated from pure TeO2, in good agreement with simulations