7,068 research outputs found
Physics Avoidance & Cooperative Semantics: Inferentialism and Mark Wilsonâs Engagement with Naturalism Qua Applied Mathematics
Mark Wilson argues that the standard categorizations of "Theory T thinking"â logic-centered conceptions of scientific organization (canonized via logical empiricists in the mid-twentieth century)âdampens the understanding and appreciation of those strategic subtleties working within science. By "Theory T thinking," we mean to describe the simplistic methodology in which mathematical science allegedly supplies âprocessesâ that parallel nature's own in a tidily isomorphic fashion, wherein "Theory Tâs" feigned rigor and methodological dogmas advance inadequate discrimination that fails to distinguish between explanatory structures that are architecturally distinct. One of Wilson's main goals is to reverse such premature exclusions and, thus, early on Wilson returns to John Locke's original physical concerns regarding material science and the congeries of descriptive concern insofar as capturing varied phenomena (i.e., cohesion, elasticity, fracture, and the transmission of coherent work) encountered amongst ordinary solids like wood and steel are concerned. Of course, Wilson methodologically updates such a purview by appealing to multiscalar techniques of modern computing, drawing from Robert Batterman's work on the greediness of scales and Jim Woodward's insights on causation
Psychophysical investigations of visual density discrimination
Work in spatial vision is reviewed and a new effect of spatial averaging is reported. This shows that dot separation discriminations are improved if the cue is represented in the intervals within a collection of dots arranged in a lattice, compared to simple 2 dot separation discriminations. This phenomenon may be related to integrative processes that mediate texture density estimation.
Four models for density discrimination are described. One involves measurements of spatial filter outputs. Computer simulations show that in principle, density cues can be encoded by a system of four DOG filters with peak sensitivities spanning a range of 3 octaves.
Alternative models involve operations performed over representations in which spatial features are made explicit. One of these involves estimations of numerosity or coverage of the texture elements. Another involves averaging of the interval values between adjacent elements. A neural model for measuring the relevant intervals is described.
It is argued that in principle the input to a density processor does not require the full sequence of operations in the MIRAGE transformation (eg. Watt and Morgan 1985). In particular, the regions of activity in the second derivative do not need to be interpreted in terms of edges, bars and blobs in order for density estimation to commence. This also implies that explicit coding of texture elements may be unnecessary.
Data for density discrimination in regular and random dot patterns are reported. These do not support the coverage and counting models and observed performance shows significant departures from predictions based on an analysis of the statistics of the interval distribution in the stimuli. But this result can be understood in relation to other factors in the interval averaging process, and there is empirical support for the hypothesized method for measuring the intervals.
Other experiments show that density is scaled according to stimulus size and possibly perceived depth. It is also shown that information from density analysis can be combined with size estimations to produce highly accurate discriminations of image expansion or object depth changes
"Magic" numbers in Smale's 7th problem
Smale's 7-th problem concerns N-point configurations on the 2-dim sphere
which minimize the logarithmic pair-energy V_0(r) = -ln r averaged over the
pairs in a configuration; here, r is the chordal distance between the points
forming a pair. More generally, V_0(r) may be replaced by the standardized
Riesz pair-energy V_s(r)= (r^{-s} -1)/s, which becomes - ln r in the limit s to
0, and the sphere may be replaced by other compact manifolds. This paper
inquires into the concavity of the map from the integers N>1 into the minimal
average standardized Riesz pair-energies v_s(N) of the N-point configurations
on the 2-sphere for various real s. It is known that v_s(N) is strictly
increasing for each real s, and for s<2 also bounded above, hence "overall
concave." It is (easily) proved that v_{-2}(N) is even locally strictly
concave, and that so is v_s(2n) for s<-2. By analyzing computer-experimental
data of putatively minimal average Riesz pair-energies v_s^x(N) for s in
{-1,0,1,2,3} and N in {2,...,200}, it is found that {v}_{-1}^x(N) is locally
strictly concave, while v_s^x(N) is not always locally strictly concave for s
in {0,1,2,3}: concavity defects occur whenever N in C^{x}_+(s) (an s-specific
empirical set of integers). It is found that the empirical map C^{x}_+(s), with
s in {-2,-1,0,1,2,3}, is set-theoretically increasing; moreover, the percentage
of odd numbers in C^{x}_+(s), s in {0,1,2,3}, is found to increase with s. The
integers in C^{x}_+(0) are few and far between, forming a curious sequence of
numbers, reminiscent of the "magic numbers" in nuclear physics. It is
conjectured that the "magic numbers" in Smale's 7-th problem are associated
with optimally symmetric optimal-energy configurations.Comment: 109 pages, of which 30 are numerical data tables. Thoroughly revised
version, to appear in J. Stat. Phys. under the different title: `Optimal N
point configurations on the sphere: "Magic" numbers and Smale's 7th problem
The spin gap in malachite Cu2(OH)2CO3 and its evolution under pressure
We report on the microscopic magnetic modeling of the spin-1/2 copper mineral
malachite at ambient and elevated pressures. Despite the layered crystal
structure of this mineral, the ambient-pressure susceptibility and
magnetization data can be well described by an unfrustrated
quasi-one-dimensional magnetic model. Weakly interacting antiferromagnetic
alternating spin chains are responsible for a large spin gap of 120K. Although
the intradimer Cu-O-Cu bridging angles are considerably smaller than the
interdimer angles, density functional theory (DFT) calculations revealed that
the largest exchange coupling of 190K operates within the structural dimers.
The lack of the inversion symmetry in the exchange pathways gives rise to
sizable Dzyaloshinskii-Moriya interactions which were estimated by
full-relativistic DFT+U calculations. Based on available high-pressure crystal
structures, we investigate the exchange couplings under pressure and make
predictions for the evolution of the spin gap. The calculations evidence that
intradimer couplings are strongly pressure-dependent and their evolution
underlies the decrease of the spin gap under pressure. Finally, we assess the
accuracy of hydrogen positions determined by structural relaxation within DFT
and put forward this computational method as a viable alternative to elaborate
experiments
Two-nucleon emission in neutrino and electron scattering from nuclei: the modified convolution approximation
The theoretical formalism of inclusive lepton-nucleus scattering in the
two-nucleon emission channel is discussed in the context of a simplified
approach, the modified convolution approximation. This allows one to write the
2p2h responses of the relativistic Fermi gas as a folding integral of two 1p1h
responses with the energies and momenta transferred to each nucleon. The idea
behind this method is to introduce different average momenta for the two
initial nucleons in the matrix elements of the two-body current, with the
innovation that they depend on the transferred energies and momenta. This
method treats exactly the two-body phase space kinematics, and reduces the
formulae of the response functions from seven-dimensional integrals over
momenta to much simpler three-dimensional ones. The applicability of the method
is checked by comparing with the full results within a model of electroweak
meson-exchange currents. The predictions are accurate enough, especially in the
low-energy threshold region where the average momentum approximation works the
best.Comment: 35 pages, 13 figure
Quasi-oscillatory motion of single cells on micropatterns
Zellmigration spielt eine grundlegende Rolle bei Prozessen wie Embryogenese, der Immunantwort, Wundheilung und bei der Metastasierung von Krebs. Daher ist der Mechanismus der Zellmigration, insbesondere die Dynamik des Zytoskeletts, Aktinpolymerisierung und Reaktionsdiffusionsprozesse, von groĂem Interesse fĂŒr die Lebenswissenschaften. Zellen sind hochkomplexe dynamische Systeme, die ihren Zustand stĂ€ndig verĂ€ndern, wodurch sich bestimmte Morphologien und Migrationsmodi ausprĂ€gen. Die resultierenden Migrationsmuster werden durch externe Faktoren beeinflusst, die unter klassischen Kulturbedingungen nicht kontrolliert sind. Eine zentrale Herausforderung bei der Untersuchung der Zellmigration ist daher die Entwicklung spezifischer Methoden, um die Wirkung einzelner Parameter, die das Zellverhalten regulieren, untersuchen zu können.
Ein möglicher Weg, die KomplexitĂ€t der Umgebung zu reduzieren, besteht darin, Mikrostrukturierungstechniken zu verwenden um Zellen auf eine definierte Mikroumgebung zu beschrĂ€nken. Mit solchen Strukturen kann der Freiheitsgrad der Zellbewegung reduziert werden, was es ermöglicht gezielt spezifische Eigenschaften der Zellmigration zu studieren. DarĂŒber hinaus kann man mit Mikrostrukturierungstechnologie Felder von einer groĂen Anzahl identischer funktioneller OberflĂ€chenstrukturen herstellen und so Hochdurchsatzmessungen durchfĂŒhren.
Im ersten Teil dieser Arbeit werden Studien zu einem neu entdeckten quasi-oszillatorischen Migrationsmodus von Einzelzellen auf kreisförmigen Mikrostrukturen vorgestellt. Wir beobachten persistente polarisierte Zellen und gerichtete Pol-zu-Pol-Bewegungen innerhalb der Strukturen. Die Zellen depolarisieren auf einer Seite der Mikrostuktur, gefolgt von einer verzögerten Repolarisierung in entgegengesetzter Richtung. Weiter wird gezeigt, dass mehrere Zelllinien (z.B. MDCK-, Huh7-, MDA-MB-231-Zellen) diesen oszillierenden Migrationsmodus auf kreis-, ellipsen- und streifenförmigen Mikrostrukturen zeigen. Im Vergleich zu kreisförmigen und elliptischen Strukturen ist das Auftreten von Oszillationen auf Streifen gehÀuft feststellbar.
Streifen bieten eine ideale und einfache Plattform um neue Migrationsmuster von Zellen und um den molekularen Mechanismus, der der Dynamik des Zytoskeletts zugrunde liegt, zu studieren. Im zweiten Teil dieser Arbeit analysieren wir das Zellverhalten mit Hilfe der rĂ€umlichen Geschwindigkeitsverteilung und dem Frequenzspektrum der Bewegung. Die experimentellen Daten werden mit einem zellulĂ€ren Potts-Modell verglichen, das ein minimales mechanistisches Modell des dynamischen Zytoskeletts enthĂ€lt. Insbesondere betrachten wir die Dauer des Umkehrprozesses als MaĂ fĂŒr die Dauer spontaner Repolarisierung von Zellen und fĂŒr die Zeit, die das fĂŒhrende Lamellipodium benötigt um sich am Ende des Streifens zurĂŒck zu bilden. Mit LifeAct-GFP transfizierten Zellen und Streifen mit unterschiedlich geformten Enden lassen sich VerĂ€nderungen im Verhalten an den Enden beobachten. Dies zeigt, dass die Form der Streifenenden und damit die lokale KrĂŒmmung der Zellfront Einfluss auf die Aktinpolymerisation hat. Diese Arbeit zeigt, dass Streifen fĂŒr die quantitative Untersuchung von Zellmigration nĂŒtzlich sind und dass erweiterte zellulĂ€re Potts-Modelle mit einfachen mechanistischen Regeln die unterschiedlichen MigrationsphĂ€notypen von Zellen in einer beengten Umgebung erfassen können.Cell migration plays a fundamental role in processes such as embryogenesis, immune response, wound healing and cancer metastasis. Hence the mechanisms of cell migration in particularly cytoskeleton dynamics, actin assembly, and reaction diffusion processes have received great interest in life science. Cells are highly complex dynamic systems that constantly alter their states, which leads to emerging morphologies and migratory modes. The resulting migration patterns are influenced by external cues, which are uncontrolled under classic culture conditions. Thus, a key challenge of studying cell migration is the design of specific methods to disentangle the effect of separate parameter regulating cellular behavior.
A possible way to reduce the complexity of the environment is to confine cells to a defined external microenvironment by applying micropatterning techniques. Using these geometries, the degree of freedom of the cell motion can be reduced, which allows selectively studying specific characteristics of cell migration. Moreover, micropatterning technology can realize large-scale arrays of functional surface coatings, so that high throughput measurements can be obtained. In the first part of this work, studies on a newly discovered quasi-oscillatory migration mode of single cells on isotropic circular-micropatterns are presented. We observe persistent polarized cell shapes and directed pole-to-pole motion within the patterns. Cells depolarize at one side of the given micropattern, followed by delayed repolarization progressing towards the opposite side. We then show that several cell lines (e.g. MDCK, Huh7, MDA-MB-231 cells) exhibit the oscillatory migration mode on circular-shaped, ellipse-shaped, and stripe-shaped micropatterns respectively. Compared to circular and ellipse patterns, stripe-shaped microlanes enhance the occurrence of oscillations.
Microlanes provide an ideal and simple platform for the exploration of emerging migration patterns of cells and the molecular mechanisms underlying cell cytoskeleton dynamics. In the second part of this work, we analyze cell motility by the spatial velocity distribution and frequency spectrum. The experimental data are compared to a Cellular Potts model that includes a minimal mechanistic model of the dynamical cytoskeleton. In particular, we evaluate the âreversal timeâ as a measure for spontaneous repolarization of cells as well as the time required to quench the leading lamellipodium at the microlane ends. Using LifeAct-GFP transfected cells and microlanes with differently shaped geometric ends, we found distinct scenarios at the leading edge showing that the tip geometry and hence the local deformation of the leading edge has an effect on actin polymerization. This work shows that microlanes are useful for quantitative assessment of cell migration and that extended Cellular Potts models with simple mechanistic rules capture the distinct migration phenotypes in confinement
Tunnelling of topological line defects in strongly coupled superfluids
The geometric theory of vortex tunnelling in superfluid liquids is developed.
Geometry rules the tunnelling process in the approximation of an incompressible
superfluid, which yields the identity of phase and configuration space in the
vortex collective co-ordinate. To exemplify the implications of this approach
to tunnelling, we solve explicitly for the two-dimensional motion of a point
vortex in the presence of an ellipse, showing that the hydrodynamic collective
co-ordinate description limits the constant energy paths allowed for the vortex
in configuration space. We outline the experimental procedure used in helium II
to observe tunnelling events, and compare the conclusions we draw to the
experimental results obtained so far. Tunnelling in Fermi superfluids is
discussed, where it is assumed that the low energy quasiparticle excitations
localised in the vortex core govern the vortex dynamical equations. The
tunnelling process can be dominated by Hall or dissipative terms, respectively
be under the influence of both, with a possible realization of this last
intermediate case in unconventional, high-temperature superconductors.Comment: 51 pages, 15 figures, uses Ann. Phys. (Leipzig) style file; forms
part of author's dissertation, available at
http://xxx.lanl.gov/abs/cond-mat/9909166v
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