Determining All Universal Tilers

A universal tiler is a convex polyhedron whose every cross-section tiles the plane. In this paper, we introduce a certain slight-rotating operation for cross-sections of pentahedra. Based on a selected initial cross-section and by applying the slight-rotating operation suitably, we prove that a convex polyhedron is a universal tiler if and only if it is a tetrahedron or a triangular prism.Comment: 18 pages, 12 figure

Optimal receptor-cluster size determined by intrinsic and extrinsic noise

Biological cells sense external chemical stimuli in their environment using cell-surface receptors. To increase the sensitivity of sensing, receptors often cluster, most noticeably in bacterial chemotaxis, a paradigm for signaling and sensing in general. While amplification of weak stimuli is useful in absence of noise, its usefulness is less clear in presence of extrinsic input noise and intrinsic signaling noise. Here, exemplified on bacterial chemotaxis, we combine the allosteric Monod-Wyman- Changeux model for signal amplification by receptor complexes with calculations of noise to study their interconnectedness. Importantly, we calculate the signal-to-noise ratio, describing the balance of beneficial and detrimental effects of clustering for the cell. Interestingly, we find that there is no advantage for the cell to build receptor complexes for noisy input stimuli in absence of intrinsic signaling noise. However, with intrinsic noise, an optimal complex size arises in line with estimates of the sizes of chemoreceptor complexes in bacteria and protein aggregates in lipid rafts of eukaryotic cells.Comment: 15 pages, 12 figures,accepted for publication on Physical Review

A Bichromatic Incidence Bound and an Application

We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}k^{2/3}n^{(d-2)/3} + kn^{d-2} + m) incidences between the k red points and m hyperplanes spanned by all n points provided that m = \Omega(n^{d-2}). For the monochromatic case k = n, this was proved by Agarwal and Aronov. We use this incidence bound to prove that a set of n points, no more than n-k of which lie on any plane or two lines, spans \Omega(nk^2) planes. We also provide an infinite family of counterexamples to a conjecture of Purdy's on the number of hyperplanes spanned by a set of points in dimensions higher than 3, and present new conjectures not subject to the counterexample.Comment: 12 page

Through the looking glass: counter-mirror activation following incompatible sensorimotor learning.

The mirror system, comprising cortical areas that allow the actions of others to be represented in the observer's own motor system, is thought to be crucial for the development of social cognition in humans. Despite the importance of the human mirror system, little is known about its origins. We investigated the role of sensorimotor experience in the development of the mirror system. Functional magnetic resonance imaging was used to measure neural responses to observed hand and foot actions following one of two types of training. During training, participants in the Compatible (control) group made mirror responses to observed actions (hand responses were made to hand stimuli and foot responses to foot stimuli), whereas the Incompatible group made counter-mirror responses (hand to foot and foot to hand). Comparison of these groups revealed that, after training to respond in a counter-mirror fashion, the relative action observation properties of the mirror system were reversed; areas that showed greater responses to observation of hand actions in the Compatible group responded more strongly to observation of foot actions in the Incompatible group. These results suggest that, rather than being innate or the product of unimodal visual or motor experience, the mirror properties of the mirror system are acquired through sensorimotor learning

Bend it like Beckham: embodying the motor skills of famous athletes.

Observing an action activates the same representations as does the actual performance of the action. Here we show for the first time that the action system can also be activated in the complete absence of action perception. When the participants had to identify the faces of famous athletes, the responses were influenced by their similarity to the motor skills of the athletes. Thus, the motor skills of the viewed athletes were retrieved automatically during person identification and had a direct influence on the action system of the observer. However, our results also indicated that motor behaviours that are implicit characteristics of other people are represented differently from when actions are directly observed. That is, unlike the facilitatory effects reported when actions were seen, the embodiment of the motor behaviour that is not concurrently perceived gave rise to contrast effects where responses similar to the behaviour of the athletes were inhibited

GTP and Ca2+ Modulate the Inositol 1,4,5-Trisphosphate-Dependent Ca2+ Release in Streptolysin O-Permeabilized Bovine Adrenal Chromaffin Cells

The inositol 1,4,5-trisphosphate (IP3)-induced Ca2+ release was studied using streptolysin O-permeabilized bovine adrenal chromaffin cells. The IP3-induced Ca2+ release was followed by Ca2+ reuptake into intracellular compartments. The IP3-induced Ca2+ release diminished after sequential applications of the same amount of IP3. Addition of 20 μM GTP fully restored the sensitivity to IP3. Guanosine 5'-O-(3-thio)triphosphate (GTPγS) could not replace GTP but prevented the action of GTP. The effects of GTP and GTPγS were reversible. Neither GTP nor GTPγS induced release of Ca2+ in the absence of IP3. The amount of Ca2+ whose release was induced by IP3 depended on the free Ca2+ concentration of the medium. At 0.3 μM free Ca2+, a half-maximal Ca2+ release was elicited with ∼0.1 μM IP3. At 1 μM free Ca2+, no Ca2+ release was observed with 0.1 μM IP3; at this Ca2+ concentration, higher concentrations of IP3 (0.25 μM) were required to evoke Ca2+ release. At 8 μM free Ca2+, even 0.25 μM IP3 failed to induce release of Ca2+ from the store. The IP3-induced Ca2+ release at constant low (0.2 μM) free Ca2+ concentrations correlated directly with the amount of stored Ca2+. Depending on the filling state of the intracellular compartment, 1 mol of IP3 induced release of between 5 and 30 mol of Ca2+