On the Destruction and Over-Merging of Dark Halos in Dissipationless N-body Simulations

N-body simulations that follow only a collisionless dark matter component have failed to produce galaxy halos or substructure within dense environments. We investigate the `over-merging' problem analytically and with numerical simulations, by calculating dissolution timescales of halos due to physical and artificial dynamical effects. The numerical resolution that has recently been attained is such that mass-loss from two-body relaxation is negligible. We demonstrate that substructure is destroyed in present simulations as a result of large force softening combined with the heating sources of tides and encounters with dissolving substructure. In the limit of infinite numerical resolution, whether or not individual halos or substructure can survive depends sensitively on their inner density profiles. Singular isothermal halos will always survive at some level, however, if halos form with large core radii then the over-merging problem will always exist within dissipationless N-body simulations. In this latter case a dissipational component can increase the halos central density enabling galaxies to survive.Comment: submitted to ApJL. compressed postscript file includes figures

The motivic Donaldson-Thomas invariants of (-2) curves

In this paper we calculate the motivic Donaldson-Thomas invariants for (-2)-curves arising from 3-fold flopping contractions in the minimal model programme. We translate this geometric situation into the machinery developed by Kontsevich and Soibelman, and using the results and framework developed previously by the authors we describe the monodromy on these invariants. In particular, in contrast to all existing known Donaldson-Thomas invariants for small resolutions of Gorenstein singularities these monodromy actions are nontrivial.Comment: 30 pages, 3 figure

Drosophila Photoreceptors and Signaling Mechanisms

Fly eyes have been a useful biological system in which fundamental principles of sensory signaling have been elucidated. The physiological optics of the fly compound eye, which was discovered in the Musca, Calliphora and Drosophila flies, has been widely exploited in pioneering genetic and developmental studies. The detailed photochemical cycle of bistable photopigments has been elucidated in Drosophila using the genetic approach. Studies of Drosophila phototransduction using the genetic approach have led to the discovery of novel proteins crucial to many biological processes. A notable example is the discovery of the inactivation no afterpotential D scaffold protein, which binds the light-activated channel, its activator the phospholipase C and it regulator protein kinase C. An additional protein discovered in the Drosophila eye is the light-activated channel transient receptor potential (TRP), the founding member of the diverse and widely spread TRP channel superfamily. The fly eye has thus played a major role in the molecular identification of processes and proteins with prime importance

An optimum time-stepping scheme for N-body simulations

We present a new time-stepping criterion for N-body simulations that is based on the true dynamical time of a particle. This allows us to follow the orbits of particles correctly in all environments since it has better adaptivity than previous time-stepping criteria used in N-body simulations. Furthermore, it requires far fewer force evaluations in low density regions of the simulation and has no dependence on artificial parameters such as, for example, the softening length. This can be orders of magnitude faster than conventional ad-hoc methods that employ combinations of acceleration and softening and is ideally suited for hard problems, such as obtaining the correct dynamics in the very central regions of dark matter haloes. We also derive an eccentricity correction for a general leapfrog integration scheme that can follow gravitational scattering events for orbits with eccentricity e -> 1 with high precision. These new approaches allow us to study a range of problems in collisionless and collisional dynamics from few body problems to cosmological structure formation. We present tests of the time-stepping scheme in N-body simulations of 2-body orbits with eccentricity e -> 1 (elliptic and hyperbolic), equilibrium haloes and a hierarchical cosmological structure formation run.Comment: 15 pages, 10 figures, replaced with version that matches published versio

The Utility of Large Language Models and Generative AI for Education Research

The use of natural language processing (NLP) techniques in engineering education can provide valuable insights into the underlying processes involved in generating text. While accessing these insights can be labor-intensive if done manually, recent advances in NLP and large language models have made it a realistic option for individuals. This study explores and evaluates a combination of clustering, summarization, and prompting techniques to analyze over 1,000 student essays in which students discussed their career interests. The specific assignment prompted students to define and explain their career goals as engineers. Using text embedding representations of student responses, we clustered the responses together to identify thematically similar statements from students. The clustered responses were then summarized to quickly identify career interest themes. We also used a set of a priori codes about career satisfaction and sectors to demonstrate an alternative approach to using these generative text models to analyze student writing. The results of this study demonstrate the feasibility and usefulness of NLP techniques in engineering education research. By automating the initial analysis of student essays, researchers and educators can more efficiently and accurately identify key themes and patterns in student writing. The methods presented in this paper have broader applications for engineering education and research purposes beyond analyzing student essays. By explaining these methods to the engineering education community, readers can utilize them in their own contexts.Comment: 3 figures, 10 table

Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case

Using Katz, Klemm and Vafa geometric engineering method of $\mathcal{N}=2$ supersymmetric QFT$_{4}$s and results on the classification of generalized Cartan matrices of Kac-Moody (KM) algebras, we study the un-explored class of $\mathcal{N}=2$ CFT$_{4}$s based on \textit{indefinite} singularities. We show that the vanishing condition for the general expression of holomorphic beta function of $\mathcal{N}=2$ quiver gauge QFT$_{4}$s coincides exactly with the fundamental classification theorem of KM algebras. Explicit solutions are derived for mirror geometries of CY threefolds with \textit{% hyperbolic} singularities.Comment: 23 pages, 4 figures, minor change

Open Channel Block by Ca2+ Underlies the Voltage Dependence of Drosophila TRPL Channel

The light-activated channels of Drosophila photoreceptors transient receptor potential (TRP) and TRP-like (TRPL) show voltage-dependent conductance during illumination. Recent studies implied that mammalian members of the TRP family, which belong to the TRPV and TRPM subfamilies, are intrinsically voltage-gated channels. However, it is unclear whether the Drosophila TRPs, which belong to the TRPC subfamily, share the same voltage-dependent gating mechanism. Exploring the voltage dependence of Drosophila TRPL expressed in S2 cells, we found that the voltage dependence of this channel is not an intrinsic property since it became linear upon removal of divalent cations. We further found that Ca2+ blocked TRPL in a voltage-dependent manner by an open channel block mechanism, which determines the frequency of channel openings and constitutes the sole parameter that underlies its voltage dependence. Whole cell recordings from a Drosophila mutant expressing only TRPL indicated that Ca2+ block also accounts for the voltage dependence of the native TRPL channels. The open channel block by Ca2+ that we characterized is a useful mechanism to improve the signal to noise ratio of the response to intense light when virtually all the large conductance TRPL channels are blocked and only the low conductance TRP channels with lower Ca2+ affinity are active

The Stronger Families in Australia (SFIA) study: Phase 2

This report presents a medium- to long-term evaluation of the Communities for Children (CfC) initiative. This Australian Government initiative aims to improve services for young children and their families and the communities they grow up in. The evaluation, known as the Stronger Families in Australia (SFIA) study, looks at the impact of CfC on child, family, and community outcomes. Phase 1 of the evaluation, published in 2009, found a small but positive impact of the initiative. This new report presents findings from Phase 2 of the study, which followed up 1,927 of the original study families, with the children now aged from 8-10 years old. Phase 2 also introduced a new cohort of 1,800 families and four new "contrast" sites