3,118 research outputs found
Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions
We develop general criteria that ensure that any non-zero solution of a given
second-order difference equation is differentially transcendental, which apply
uniformly in particular cases of interest, such as shift difference equations,
q-dilation difference equations, Mahler difference equations, and elliptic
difference equations. These criteria are obtained as an application of
differential Galois theory for difference equations. We apply our criteria to
prove a new result to the effect that most elliptic hypergeometric functions
are differentially transcendental
Observation of a nanophase segregation in LiCl aqueous solutions from Transient Grating Experiments
Transient Grating experiments performed on supercooled LiCl, RH2O solutions
with R>6 reveal the existence of a strong, short time, extra signal which
superposes to the normal signal observed for the R=6 solution and other glass
forming systems. This extra signal shows up below 190 K, its shape and the
associated timescale depend only on temperature, while its intensity increases
with R. We show that the origin of this signal is a phase separation between
clusters with a low solute concentration and the remaining, more concentrated,
solution. Our analysis demonstrates that these clusters have a nanometer size
and a composition which are rather temperature independent, while increasing R
simply increases the number of these clusters.Comment: 19 pages+ 8 figures+ 2 table
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
Distance Oracles for Time-Dependent Networks
We present the first approximate distance oracle for sparse directed networks
with time-dependent arc-travel-times determined by continuous, piecewise
linear, positive functions possessing the FIFO property.
Our approach precomputes approximate distance summaries from
selected landmark vertices to all other vertices in the network. Our oracle
uses subquadratic space and time preprocessing, and provides two sublinear-time
query algorithms that deliver constant and approximate
shortest-travel-times, respectively, for arbitrary origin-destination pairs in
the network, for any constant . Our oracle is based only on
the sparsity of the network, along with two quite natural assumptions about
travel-time functions which allow the smooth transition towards asymmetric and
time-dependent distance metrics.Comment: A preliminary version appeared as Technical Report ECOMPASS-TR-025 of
EU funded research project eCOMPASS (http://www.ecompass-project.eu/). An
extended abstract also appeared in the 41st International Colloquium on
Automata, Languages, and Programming (ICALP 2014, track-A
Observation of the onset of strong scattering on high frequency acoustic phonons in densified silica glass
The linewidth of longitudinal acoustic waves in densified silica glass is
obtained by inelastic x-ray scattering. It increases with a high power alpha of
the frequency up to a crossover where the waves experience strong scattering.
We find that \alpha is at least 4, and probably larger. Resonance and
hybridization of acoustic waves with the boson-peak modes seems to be a more
likely explanation for these findings than Rayleigh scattering from disorder.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Letter
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
A rolling-horizon quadratic-programming approach to the signal control problem in large-scale congested urban road networks
The paper investigates the efficiency of a recently developed signal control methodology, which offers a computationally feasible technique for real-time network-wide signal control in large-scale urban traffic networks and is applicable also under congested traffic conditions. In this methodology, the traffic flow process is modeled by use of the store-and-forward modeling paradigm, and the problem of network-wide signal control (including all constraints) is formulated as a quadratic-programming problem that aims at minimizing and balancing the link queues so as to minimize the risk of queue spillback. For the application of the proposed methodology in real time, the corresponding optimization algorithm is embedded in a rolling-horizon (model-predictive) control scheme. The control strategy’s efficiency and real-time feasibility is demonstrated and compared with the Linear-Quadratic approach taken by the signal control strategy TUC (Traffic-responsive Urban Control) as well as with optimized fixed-control settings via their simulation-based application to the road network of the city centre of Chania, Greece, under a number of different demand scenarios. The comparative evaluation is based on various criteria and tools including the recently proposed fundamental diagram for urban network traffic
“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
Revisiting the Six Stages of Skill Acquisition
The acquisition of a new skill usually proceeds through five stages, from novice to expert, with a sixth stage of mastery available for highly motivated performers. In this chapter, we re-state the six stages of the Dreyfus Skill Model, paying new attention to the transitions and interrelations between them. While discussing the fifth stage, expertise, we unpack the claim that, “when things are proceeding normally, experts don’t solve problems and don’t make decisions; they do what normally works” (Dreyfus & Dreyfus, 1988, pp. 30 – 31). This leads us to offer an account of the “perspectival deliberation” that arises for experts and masters and that is distinct from the calculative deliberation characteristic of the lower stages of skillfulness
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