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Realization spaces of 4-polytopes are universal

Let $P\subset\R^d$ be a $d$-dimensional polytope. The {\em realization space} of~$P$ is the space of all polytopes $P'\subset\R^d$ that are combinatorially equivalent to~$P$, modulo affine transformations. We report on work by the first author, which shows that realization spaces of \mbox{4-dimensional} polytopes can be ``arbitrarily bad'': namely, for every primary semialgebraic set~$V$ defined over~$\Z$, there is a $4$-polytope $P(V)$ whose realization space is ``stably equivalent'' to~$V$. This implies that the realization space of a $4$-polytope can have the homotopy type of an arbitrary finite simplicial complex, and that all algebraic numbers are needed to realize all $4$- polytopes. The proof is constructive. These results sharply contrast the $3$-dimensional case, where realization spaces are contractible and all polytopes are realizable with integral coordinates (Steinitz's Theorem). No similar universality result was previously known in any fixed dimension.Comment: 10 page

Bipedal steps in the development of rhythmic behavior in humans

We contrast two related hypotheses of the evolution of dance: H1: Maternal bipedal walking influenced the fetal experience of sound and associated movement patterns; H2: The human transition to bipedal gait produced more isochronous/predictable locomotion sound resulting in early music-like behavior associated with the acoustic advantages conferred by moving bipedally in pace. The cadence of walking is around 120 beats per minute, similar to the tempo of dance and music. Human walking displays long-term constancies. Dyads often subconsciously synchronize steps. The major amplitude component of the step is a distinctly produced beat. Human locomotion influences, and interacts with, emotions, and passive listening to music activates brain motor areas. Across dance-genres the footwork is most often performed in time to the musical beat. Brain development is largely shaped by early sensory experience, with hearing developed from week 18 of gestation. Newborns reacts to sounds, melodies, and rhythmic poems to which they have been exposed in utero. If the sound and vibrations produced by footfalls of a walking mother are transmitted to the fetus in coordination with the cadence of the motion, a connection between isochronous sound and rhythmical movement may be developed. Rhythmical sounds of the human mother locomotion differ substantially from that of nonhuman primates, while the maternal heartbeat heard is likely to have a similar isochronous character across primates, suggesting a relatively more influential role of footfall in the development of rhythmic/musical abilities in humans. Associations of gait, music, and dance are numerous. The apparent absence of musical and rhythmic abilities in nonhuman primates, which display little bipedal locomotion, corroborates that bipedal gait may be linked to the development of rhythmic abilities in humans. Bipedal stimuli in utero may primarily boost the ontogenetic development. The acoustical advantage hypothesis proposes a mechanism in the phylogenetic development

A machine learning approach to the Berezinskii-Kosterlitz-Thouless transition in classical and quantum models

The Berezinskii-Kosterlitz-Thouless transition is a very specific phase transition where all thermodynamic quantities are smooth. Therefore, it is difficult to determine the critical temperature in a precise way. In this paper we demonstrate how neural networks can be used to perform this task. In particular, we study how the accuracy of the transition identification depends on the way the neural networks are trained. We apply our approach to three different systems: (i) the classical XY model, (ii) the phase-fermion model, where classical and quantum degrees of freedom are coupled and (iii) the quantum XY model.Comment: 11 pages, 7 figure

Comment on "Density of States and Critical Behavior of the Coulomb Glass"

In a recent numerical investigation of the Coulomb glass, Surer et al. [Phys. Rev. Lett. 102, 067205 (2009)] concluded that their simulation results are consistent with the Efros Shklovskii prediction for the density of states in the three-dimensional case. Here, we show that this statement has no relevance concerning the problem of the asymptotic behavior in the Coulomb gap since it is based on unjustified assumptions. Moreover, for the random-displacement Coulomb glass model, we demonstrate that a part of the density of states data by Surer et al. erroneously exhibit a broad gap. This is related to the staggered occupation being instable contrary to their findings.Comment: Submitted to Physical Review Letters, 1 page, 1 figur

Advancing the Empirical Research on Lobbying

This essay identifies the empirical facts about lobbying which are generally agreed upon in the literature. It then discusses challenges to empirical research in lobbying and provides examples of empirical methods that can be employed to overcome these challenges—with an emphasis on statistical measurement, identification, and casual inference. The essay then discusses the advantages, disadvantages, and effective use of the main types of data available for research in lobbying. It closes by discussing a number of open questions for researchers in the field and avenues for future work to advance the empirical research in lobbying

Comment on Zwally and others (2015)-mass gains of the Antarctic ice sheet exceed losses

In their article ‘Mass gains of the Antarctic ice sheet exceed losses’ Zwally and others (2015) choose Vostok Subglacial Lake as an exemplary region to demonstrate their inference of surface height change rates from a portion of the ICESat mission’s laser altimetry data (2003–08). In their appendix, they discuss some of the remarkable differences between their results and those reported by Richter and others (2008, 2013, 2014). However, the selective consideration of our works and the misleading or incorrect interpretation of our results call for clarificationFil: Richter, Andreas Jorg. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Technische Universitaet Dresden; AlemaniaFil: Horwath, M.. Technische Universitaet Dresden; AlemaniaFil: Dietrich, R.. Technische Universitaet Dresden; Alemani

Semiclassical Theory of Chaotic Quantum Transport

We present a refined semiclassical approach to the Landauer conductance and Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for systems with uniformly hyperbolic dynamics that including off-diagonal contributions to double sums over classical paths gives a weak-localization correction in quantitative agreement with results from random matrix theory. We further discuss the magnetic field dependence. This semiclassical treatment accounts for current conservation.Comment: 4 pages, 1 figur

Large Negative Electronic Compressibility of LaAlO3-SrTiO3 Interfaces with Ultrathin LaAlO3 Layers

A two-dimensional electron liquid is formed at the n-type interface between SrTiO3 and LaAlO3. Here we report on Kelvin probe microscopy measurements of the electronic compressibility of this electron system. The electronic compressibility is found to be negative for carrier densities of \approx10^13/cm^2. At even smaller densities, a metal-to-insulator transition occurs. These local measurements corroborate earlier measurements of the electronic compressibility of LaAlO3-SrTiO3 interfaces obtained by measuring the capacitance of macroscopic metal-LaAlO3-SrTiO3 capacitors