Geometric representations for minimalist grammars

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we illustrate our findings by means of two particular arithmetic and fractal representations.Comment: 43 pages, 4 figure

Particle size dependence of magnetization and phase transition near T_N in multiferroic BiFeO3

We report results of a comprehensive study of the phase transition at T_N (~643 K) as a function of particle size in multiferroic BiFeO3 system. We employed electrical, thermal, and temperature dependent X-ray diffraction (XRD) studies in order to characterize the transition in a host of samples. We also carried out detailed magnetic measurements over a temperature regime 2-300 K under a magnetic field 100-10000 Oe both on bulk and nano-crystalline systems. While in the bulk system a sharp endothermic peak at T_N together with a broad feature, ranging over nearly ~150 K (Delta_T), could be observed in calorimetry, the nanoscale systems exhibit only the broad feature. The characteristic dielectric anomaly, expected at T_N, is found to occur both at T_O and T_N across Delta_T in the bulk sample. The Maxwell-Wagner component due to interfaces between heterogenous regions with different conductivities is also present. The magnetic properties, measured at lower temperature, corroborate our observations in calorimetry. The metastability increases in the nanoscale BiFeO3 with divergence between zero-field cooled (ZFC) and field cooled (FC) magnetization below ~100 K and faster magnetic relaxation. Interestingly, in nanoscale BiFeO3, one also observes finite coercivity at lower temperature which points out that suitable design of particle size and shape may induce ferromagnetism. The inhomogeneous distribution of Bi/Fe-ions and/or oxygen non-stoichiometry seems to be giving rise to broad features in thermal, magnetic as well as in electrical responses.Comment: 22 pages including 9 figures, pdf only, submitted to J. Appl. Phy

Diffusion Processes on Small-World Networks with Distance-Dependent Random-Links

We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in task-completion networks, and gradient driven transport on networks. Changing the parameters of the distance-dependence, we found a rich phase diagram, with different transient and recurrent phases in the context of random walks on networks. We performed the calculations in two limiting cases: in the annealed case, where the rearrangement of the random links is fast, and in the quenched case, where the link rearrangement is slow compared to the motion of the random walker or the surface. It has been well-established that in a large class of interacting systems, adding an arbitrarily small density of, possibly long-range, quenched random links to a regular lattice interaction topology, will give rise to mean-field (or annealed) like behavior. In some cases, however, mean-field scaling breaks down, such as in diffusion or in the Edwards-Wilkinson process in "low-dimensional" small-world networks. This break-down can be understood by treating the random links perturbatively, where the mean-field (or annealed) prediction appears as the lowest-order term of a naive perturbation expansion. The asymptotic analytic results are also confirmed numerically by employing exact numerical diagonalization of the network Laplacian. Further, we construct a finite-size scaling framework for the relevant observables, capturing the cross-over behaviors in finite networks. This work provides a detailed account of the self-consistent-perturbative and renormalization approaches briefly introduced in two earlier short reports.Comment: 36 pages, 27 figures. Minor revisions in response to the referee's comments. Furthermore, some typos were fixed and new references were adde

Categorial Compositionality: A Category Theory Explanation for the Systematicity of Human Cognition

Classical and Connectionist theories of cognitive architecture seek to explain systematicity (i.e., the property of human cognition whereby cognitive capacity comes in groups of related behaviours) as a consequence of syntactically and functionally compositional representations, respectively. However, both theories depend on ad hoc assumptions to exclude specific instances of these forms of compositionality (e.g. grammars, networks) that do not account for systematicity. By analogy with the Ptolemaic (i.e. geocentric) theory of planetary motion, although either theory can be made to be consistent with the data, both nonetheless fail to fully explain it. Category theory, a branch of mathematics, provides an alternative explanation based on the formal concept of adjunction, which relates a pair of structure-preserving maps, called functors. A functor generalizes the notion of a map between representational states to include a map between state transformations (or processes). In a formal sense, systematicity is a necessary consequence of a higher-order theory of cognitive architecture, in contrast to the first-order theories derived from Classicism or Connectionism. Category theory offers a re-conceptualization for cognitive science, analogous to the one that Copernicus provided for astronomy, where representational states are no longer the center of the cognitive universe—replaced by the relationships between the maps that transform them

Modeling of dielectric hysteresis loops in ferroelectric semiconductors with charged defects

We have proposed the phenomenological description of dielectric hysteresis loops in ferroelectric semiconductors with charged defects and prevailing extrinsic conductivity. Exactly we have modified Landau-Ginsburg approach and shown that the macroscopic state of the aforementioned inhomogeneous system can be described by three coupled equations for three order parameters. Both the experimentally observed coercive field values well below the thermodynamic one and the various hysteresis loop deformations (constricted and double loops) have been obtained in the framework of our model. The obtained results quantitatively explain the ferroelectric switching in such ferroelectric materials as thick PZT films.Comment: 21 pages, 10 figures, sent to Journal of Physics: Condensed Matte

High temperature dielectric ceramics: a review of temperature-stable high-permittivity perovskites

Recent developments are reviewed in the search for dielectric ceramics which can operate at temperatures >200 °C, well above the limit of existing high volumetric efficiency capacitor materials. Compositional systems based on lead-free relaxor dielectrics with mixed cation site occupancy on the perovskite lattice are summarised, and properties compared. As a consequence of increased dielectric peak broadening and shifts to peak temperatures, properties can be engineered such that a plateau in relative permittivity–temperature response (εr–T) is obtained, giving a ±15 %, or better, consistency in εr over a wide temperature range. Materials with extended upper temperature limits of 300, 400 and indeed 500 °C are grouped in this article according to the parent component of the solid solution, for example BaTiO3 and Na0.5Bi0.5TiO3. Challenges are highlighted in achieving a lower working temperature of −55 °C, whilst also extending the upper temperature limit of stable εr to ≥300 °C, and achieving high-permittivity and low values of dielectric loss tangent, tan δ. Summary tables and diagrams are used to help compare values of εr, tan δ, and temperature ranges of stability for different material

Employed But Still Unhappy? On the Relevance of the Social Work Norm

In the modern welfare state, people who cannot make a living usually receive financial assistance from public funds. Accordingly, the so-called social work norm against living off other people is violated, which may be the reason why the unemployed are so unhappy. If so, however, labour market concepts based on the notion of promoting low-paid jobs that are subsidised if necessary with additional payments would appear far less favourable. It could be that people are employed, but still unhappy. Using German panel data, this paper examines the relevance of the social work norm and finds a significant disutility effect of living off public funds. Although this is true for employed people as well, the results show that the individual is generally better off having a job that requires additional assistance, than having no job at all. On the other hand, such policies as the recent German labour market reforms can trigger undesired side-effects, if policy-makers ignore the issue of the social work norm

Looking the Part: Social Status Cues Shape Race Perception

It is commonly believed that race is perceived through another's facial features, such as skin color. In the present research, we demonstrate that cues to social status that often surround a face systematically change the perception of its race. Participants categorized the race of faces that varied along White–Black morph continua and that were presented with high-status or low-status attire. Low-status attire increased the likelihood of categorization as Black, whereas high-status attire increased the likelihood of categorization as White; and this influence grew stronger as race became more ambiguous (Experiment 1). When faces with high-status attire were categorized as Black or faces with low-status attire were categorized as White, participants' hand movements nevertheless revealed a simultaneous attraction to select the other race-category response (stereotypically tied to the status cue) before arriving at a final categorization. Further, this attraction effect grew as race became more ambiguous (Experiment 2). Computational simulations then demonstrated that these effects may be accounted for by a neurally plausible person categorization system, in which contextual cues come to trigger stereotypes that in turn influence race perception. Together, the findings show how stereotypes interact with physical cues to shape person categorization, and suggest that social and contextual factors guide the perception of race