When is Freshman\u27s Dream Actually True?

We address the problem of determining what points in a field satisfy Freshman\u27s Dream, or equivalently, when a monomial behaves additively. It is conjectured that the only additive points over the rational numbers are trivial. In the case of finite fields, we generalize well-known results about uni-variate polynomials to bivariate homogeneous polynomials in order to count the number of additive points

Constructing Mutually Unbiased Bases in Dimension Six

The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard matrix, we construct all others mutually unbiased to it, using algebraic computations performed by a computer program. We repeat this calculation many times, sampling all known complex Hadamard matrices, and we never find more than two that are mutually unbiased. This result adds considerable support to the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical approximations and corrected the number of triples existing for non-affine families (cf Table 3

Statistics of extinction and survival in Lotka-Volterra systems

We analyze purely competitive many-species Lotka-Volterra systems with random interaction matrices, focusing the attention on statistical properties of their asymptotic states. Generic features of the evolution are outlined from a semiquantitative analysis of the phase-space structure, and extensive numerical simulations are performed to study the statistics of the extinctions. We find that the number of surviving species depends strongly on the statistical properties of the interaction matrix, and that the probability of survival is weakly correlated to specific initial conditions.Comment: Previous version had error in authors. 11 pages, including 5 figure

Ecological model of extinctions

We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the others, that reproduces and evolves in time. Each species is simultaneously a predator and a prey in a food chain. Mutations that change the interactions are supposed to occur randomly at a low rate. Extinctions of populations result naturally from the predator-prey dynamics. The model is not pinned in a fitness variable, and natural selection arises from the dynamics.Comment: 16 pages (LaTeX type, RevTeX style), including 6 figures in gif format. To be published in Phys. Rev. E (prob. Dic. 96

Dynamics-based centrality for general directed networks

Determining the relative importance of nodes in directed networks is important in, for example, ranking websites, publications, and sports teams, and for understanding signal flows in systems biology. A prevailing centrality measure in this respect is the PageRank. In this work, we focus on another class of centrality derived from the Laplacian of the network. We extend the Laplacian-based centrality, which has mainly been applied to strongly connected networks, to the case of general directed networks such that we can quantitatively compare arbitrary nodes. Toward this end, we adopt the idea used in the PageRank to introduce global connectivity between all the pairs of nodes with a certain strength. Numerical simulations are carried out on some networks. We also offer interpretations of the Laplacian-based centrality for general directed networks in terms of various dynamical and structural properties of networks. Importantly, the Laplacian-based centrality defined as the stationary density of the continuous-time random walk with random jumps is shown to be equivalent to the absorption probability of the random walk with sinks at each node but without random jumps. Similarly, the proposed centrality represents the importance of nodes in dynamics on the original network supplied with sinks but not with random jumps.Comment: 7 figure

Terror, War, and the Economy in George W. Bush’s Approval Ratings: The Importance of Salience in Presidential Approval

George W. Bush\u27s presidency provides a fertile ground to further develop the standard model of presidential approval. In contrast to the vast presidential approval literature, early studies of Bush conclude economic conditions had no effect once the war in Iraq began. Rather than require a fundamental rethinking of presidential approval theories, we argue that approval models must take into account issue salience. When a factor is salient, it has a stronger effect. During the Bush presidency, with considerable over-time variation in the salience of the economy, terrorism, and the war in Iraq, each, in turn, powerfully affected Bush\u27s approval

Research in Pediatric Residency: National Experience of Pediatric Chief Residents

Objective To determine factors associated with increased research productivity, satisfaction, and perceived barriers to research within residency from the experience of pediatric chief residents. Methods An online cross-sectional survey was administered to academic year 2014–15 chief residents. Topics assessed included program demographic characteristics, career intentions, research productivity, satisfaction with research training and opportunities, and research barriers. Chi-square and Fisher exact tests were used for descriptive statistics. Multivariable logistic regression analysis was used to determine factors associated with productivity and research satisfaction. Results The response rate was 63% (165 of 261). Half (82 of 165) were productive in research. Most were satisfied with their quality of research training (55%; 90 of 165) and research opportunities (69%; 114 of 165). Chiefs reporting interest in research were 5 times more likely to be productive than those who did not (odds ratio [OR] = 5.2; 95% confidence interval [CI], 2.3–11.8). Productive chiefs were more likely to report including research time in future careers (P = .003). Most (83%; 137 of 165) thought their programs were supportive of resident research, but lack of time was frequently cited as a major barrier. Those satisfied with research opportunities were less likely to find lack of training (OR = 0.3; 95% CI, 0.1–0.7) or faculty mentorship (OR = 0.2; 95% CI, 0.0–0.9) as a major barrier. Conclusions Pediatric chief resident interest in research is strongly associated with research productivity during residency, and research productivity is strongly associated with career plans including research time. By cultivating research interest through faculty mentorship, research training, and dedicated time, pediatric residency programs might help foster early research success and, potentially lead to continued engagement with research in trainees' future careers

Conformational transitions of the sodium-dependent sugar transporter, vSGLT.

Sodium-dependent transporters couple the flow of Na+ ions down their electrochemical potential gradient to the uphill transport of various ligands. Many of these transporters share a common core structure composed of a five-helix inverted repeat and deliver their cargo utilizing an alternating-access mechanism. A detailed characterization of inward-facing conformations of the Na+-dependent sugar transporter from Vibrio parahaemolyticus (vSGLT) has previously been reported, but structural details on additional conformations and on how Na+ and ligand influence the equilibrium between other states remains unknown. Here, double electron-electron resonance spectroscopy, structural modeling, and molecular dynamics are utilized to deduce ligand-dependent equilibria shifts of vSGLT in micelles. In the absence and presence of saturating amounts of Na+, vSGLT favors an inward-facing conformation. Upon binding both Na+ and sugar, the equilibrium shifts toward either an outward-facing or occluded conformation. While Na+ alone does not stabilize the outward-facing state, gating charge calculations together with a kinetic model of transport suggest that the resting negative membrane potential of the cell, absent in detergent-solubilized samples, may stabilize vSGLT in an outward-open conformation where it is poised for binding external sugars. In total, these findings provide insights into ligand-induced conformational selection and delineate the transport cycle of vSGLT