Characterizing Pixel and Point Patterns with a Hyperuniformity Disorder Length

We introduce the concept of a hyperuniformity disorder length that controls the variance of volume fraction fluctuations for randomly placed windows of fixed size. In particular, fluctuations are determined by the average number of particles within a distance $h$ from the boundary of the window. We first compute special expectations and bounds in $d$ dimensions, and then illustrate the range of behavior of $h$ versus window size $L$ by analyzing three different types of simulated two-dimensional pixel pattern - where particle positions are stored as a binary digital image in which pixels have value zero/one if empty/contain a particle. The first are random binomial patterns, where pixels are randomly flipped from zero to one with probability equal to area fraction. These have long-ranged density fluctuations, and simulations confirm the exact result $h=L/2$. Next we consider vacancy patterns, where a fraction $f$ of particles on a lattice are randomly removed. These also display long-range density fluctuations, but with $h=(L/2)(f/d)$ for small $f$. For a hyperuniform system with no long-range density fluctuations, we consider Einstein patterns where each particle is independently displaced from a lattice site by a Gaussian-distributed amount. For these, at large $L$, $h$ approaches a constant equal to about half the root-mean-square displacement in each dimension. Then we turn to grayscale pixel patterns that represent simulated arrangements of polydisperse particles, where the volume of a particle is encoded in the value of its central pixel. And we discuss the continuum limit of point patterns, where pixel size vanishes. In general, we thus propose to quantify particle configurations not just by the scaling of the density fluctuation spectrum but rather by the real-space spectrum of $h(L)$ versus $L$. We call this approach Hyperuniformity Disorder Length Spectroscopy

Preparation as Prevention – Reducing Morbidity and Mortality in the Vermont Outdoors

While precipitants and outcomes of wilderness medical emergencies are numerous and diverse, wilderness rescues in Vermont are most often called for individuals or groups inadequately prepared for conditions or contingencies. In many cases, failure to bring one of a few key items such as equipment for navigation or illumination after dark can create a preventable emergency with subsequent requirement for rescue or retrieval.https://scholarworks.uvm.edu/fmclerk/1522/thumbnail.jp

Students' mental prototypes for functions and graphs

This research study investigates the concept of function developed by students studying English A-level mathematics. It shows that, while students may be able to use functions in their practical mathematics, their grasp of the theoretical nature of the function concept may be tenuous and inconsistent. The hypothesis is that students develop prototypes for the function concept in much the same way as they develop prototypes for concepts in everyday life. The definition of the function concept, though given in the curriculum, is not stressed and proves to be inoperative, with their understanding of the concept reliant on properties of familiar prototype examples: those having regular shaped graphs, such as x2 or sin*, those often encountered (possibly erroneously), such as a circle, those in which y is defined as an explicit formula in x, and so on. Investigations reveal significant misconceptions. For example, threequarters of a sample of students starting a university mathematics course considered that a constant function was not a function in either its graphical or algebraic forms, and threequarters thought that a circle is a function. This reveals a wide gulf between the concepts as perceived to be taught and as actually learned by the students

“The end of The Dreyfus affair”: (Post)Heideggerian meditations on man, machine and meaning

In this paper, the possibility of developing a Heideggerian solution to the Schizophrenia Problem associated with cognitive technologies is investigated. This problem arises as a result of the computer bracketing emotion from cognition during human-computer interaction and results in human psychic self-amputation. It is argued that in order to solve the Schizophrenia Problem, it is necessary to first solve the 'hard problem' of consciousness since emotion is at least partially experiential. Heidegger's thought, particularly as interpreted by Hubert Dreyfus, appears relevant in this regard since it ostensibly provides the basis for solving the 'hard problem' via the construction of artificial systems capable of the emergent generation of conscious experience. However, it will be shown that Heidegger's commitment to a non-experiential conception of nature renders this whole approach problematic, thereby necessitating consideration of alternative, post-Heideggerian approaches to solving the Schizophrenia Problem

Reorientational relaxation of a linear probe molecule in a simple glassy liquid

Within the mode-coupling theory (MCT) for the evolution of structural relaxation in glass-forming liquids, correlation functions and susceptibility spectra are calculated characterizing the rotational dynamics of a top-down symmetric dumbbell molecule, consisting of two fused hard spheres immersed in a hard-sphere system. It is found that for sufficiently large dumbbell elongations, the dynamics of the probe molecule follows the same universal glass-transition scenario as known from the MCT results of simple liquids. The $\alpha$-relaxation process of the angular-index-j=1 response is stronger, slower and less stretched than the one for j=2, in qualitative agreement with results found by dielectric-loss and depolarized-light-scattering spectroscopy for some supercooled liquids. For sufficiently small elongations, the reorientational relaxation occurs via large-angle flips, and the standard scenario for the glass-transition dynamics is modified for odd-j responses due to precursor phenomena of a nearby type-A MCT transition. In this case, a major part of the relaxation outside the transient regime is described qualitatively by the $\beta$-relaxation scaling laws, while the $\alpha$-relaxation scaling law is strongly disturbed.Comment: 40 pages. 10 figures as GIF-files, to be published in Phys. Rev.

A Bow of Blue / music by Max Dreyfus; words by Maurice J. Steinberg

Cover: drawing of a young lady taking a promenade, as a cherubim touches a blue bow in her hair; text reads: Supplement to the Newark Sunday News, June 9th, 1901; Publisher: T. B. Harms and Co. (New York)https://egrove.olemiss.edu/sharris_b/1008/thumbnail.jp

NEXUS/Physics: An interdisciplinary repurposing of physics for biologists

In response to increasing calls for the reform of the undergraduate science curriculum for life science majors and pre-medical students (Bio2010, Scientific Foundations for Future Physicians, Vision & Change), an interdisciplinary team has created NEXUS/Physics: a repurposing of an introductory physics curriculum for the life sciences. The curriculum interacts strongly and supportively with introductory biology and chemistry courses taken by life sciences students, with the goal of helping students build general, multi-discipline scientific competencies. In order to do this, our two-semester NEXUS/Physics course sequence is positioned as a second year course so students will have had some exposure to basic concepts in biology and chemistry. NEXUS/Physics stresses interdisciplinary examples and the content differs markedly from traditional introductory physics to facilitate this. It extends the discussion of energy to include interatomic potentials and chemical reactions, the discussion of thermodynamics to include enthalpy and Gibbs free energy, and includes a serious discussion of random vs. coherent motion including diffusion. The development of instructional materials is coordinated with careful education research. Both the new content and the results of the research are described in a series of papers for which this paper serves as an overview and context.Comment: 12 page

Dynamics at a smeared phase transition

We investigate the effects of rare regions on the dynamics of Ising magnets with planar defects, i.e., disorder perfectly correlated in two dimensions. In these systems, the magnetic phase transition is smeared because static long-range order can develop on isolated rare regions. We first study an infinite-range model by numerically solving local dynamic mean-field equations. Then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean-field theory. In the tail region of the smeared transition the dynamics is even slower than in a conventional Griffiths phase: the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times.Comment: 10 pages, 8eps figures included, final version as publishe

Light scattering spectra of supercooled molecular liquids

The light scattering spectra of molecular liquids are derived within a generalized hydrodynamics. The wave vector and scattering angle dependences are given in the most general case and the change of the spectral features from liquid to solidlike is discussed without phenomenological model assumptions for (general) dielectric systems without long-ranged order. Exact microscopic expressions are derived for the frequency-dependent transport kernels, generalized thermodynamic derivatives and the background spectra.Comment: 12 page

Cognition in Context: Phenomenology, Situated Robotics and the Frame Problem

The frame problem is the difficulty of explaining how non-magical systems think and act in ways that are adaptively sensitive to context-dependent relevance. Influenced centrally by Heideggerian phenomenology, Hubert Dreyfus has argued that the frame problem is, in part, a consequence of the assumption (made by mainstream cognitive science and artificial intelligence) that intelligent behaviour is representation-guided behaviour. Dreyfus’ Heideggerian analysis suggests that the frame problem dissolves if we reject representationalism about intelligence and recognize that human agents realize the property of thrownness (the property of being always already embedded in a context). I argue that this positive proposal is incomplete until we understand exactly how the properties in question may be instantiated in machines like us. So, working within a broadly Heideggerian conceptual framework, I pursue the character of a representationshunning thrown machine. As part of this analysis, I suggest that the frame problem is, in truth, a two-headed beast. The intra-context frame problem challenges us to say how a purely mechanistic system may achieve appropriate, flexible and fluid action within a context. The inter-context frame problem challenges us to say how a purely mechanistic system may achieve appropriate, flexible and fluid action in worlds in which adaptation to new contexts is open-ended and in which the number of potential contexts is indeterminate. Drawing on the field of situated robotics, I suggest that the intra-context frame problem may be neutralized by systems of special purpose adaptive couplings, while the inter-context frame problem may be neutralized by systems that exhibit the phenomenon of continuous reciprocal causation. I also defend the view that while continuous reciprocal causation is in conflict with representational explanation, special-purpose adaptive coupling, as well as its associated agential phenomenology, may feature representations. My proposal has been criticized recently by Dreyfus, who accuses me of propagating a cognitivist misreading of Heidegger, one that, because it maintains a role for representation, leads me seriously astray in my handling of the frame problem. I close by responding to Dreyfus’ concerns