Experimental evidence for the influence of structure and meaning on linear order in the noun phrase

Recent work has used artificial language experiments to argue that hierarchical representations drive learners’ expectations about word order in complex noun phrases like these two green cars (Culbertson & Adger 2014; Martin, Ratitamkul, et al. 2019). When trained on a novel language in which individual modifiers come after the Noun, English speakers overwhelmingly assume that multiple nominal modifiers should be ordered such that Adjectives come closest to the Noun, then Numerals, then Demonstratives (i.e., N-Adj-Num-Dem or some subset thereof). This order transparently reflects a constituent structure in which Adjectives combine with Nouns to the exclusion of Numerals and Demonstratives, and Numerals combine with Noun+Adjective units to the exclusion of Demonstratives. This structure has also been claimed to derive frequency asymmetries in complex noun phrase order across languages (e.g., Cinque 2005). However, we show that features of the methodology used in these experiments potentially encourage participants to use a particular metalinguistic strategy that could yield this outcome without implicating constituency structure. Here, we use a more naturalistic artificial language learning task to investigate whether the preference for hierarchy-respecting orders is still found when participants do not use this strategy. We find that the preference still holds, and, moreover, as Culbertson & Adger (2014) speculate, that its strength reflects structural distance between modifiers. It is strongest when ordering Adjectives relative to Demonstratives, and weaker when ordering Numerals relative to Adjectives or Demonstratives relative to Numerals. Our results provide the strongest evidence yet for the psychological influence of hierarchical structure on word order preferences during learning

Structured matrices, continued fractions, and root localization of polynomials

We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total positivity, and root localization of univariate polynomials. Along with a survey of many classical facts, we provide a number of new results.Comment: 79 pages; new material added to the Introductio

Enhancement of the Binding Energy of Charged Excitons in Disordered Quantum Wires

Negatively and positively charged excitons are identified in the spatially-resolved photoluminescence spectra of quantum wires. We demonstrate that charged excitons are weakly localized in disordered quantum wires. As a consequence, the enhancement of the "binding energy" of a charged exciton is caused, for a significant part, by the recoil energy transferred to the remaining charged carrier during its radiative recombination. We discover that the Coulomb correlation energy is not the sole origin of the "binding energy", in contrast to charged excitons confined in quantum dots.Comment: 4 Fig

New coins from old, smoothly

Given a (known) function $f:[0,1] \to (0,1)$, we consider the problem of simulating a coin with probability of heads $f(p)$ by tossing a coin with unknown heads probability $p$, as well as a fair coin, $N$ times each, where $N$ may be random. The work of Keane and O'Brien (1994) implies that such a simulation scheme with the probability $\P_p(N<\infty)$ equal to 1 exists iff $f$ is continuous. Nacu and Peres (2005) proved that $f$ is real analytic in an open set $S \subset (0,1)$ iff such a simulation scheme exists with the probability $\P_p(N>n)$ decaying exponentially in $n$ for every $p \in S$. We prove that for $\alpha>0$ non-integer, $f$ is in the space $C^\alpha [0,1]$ if and only if a simulation scheme as above exists with $\P_p(N>n) \le C (\Delta_n(p))^\alpha$, where \Delta_n(x)\eqbd \max \{\sqrt{x(1-x)/n},1/n \}. The key to the proof is a new result in approximation theory: Let \B_n be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree $n$. We show that a function $f:[0,1] \to (0,1)$ is in $C^\alpha [0,1]$ if and only if $f$ has a series representation $\sum_{n=1}^\infty F_n$ with F_n \in \B_n and $\sum_{k>n} F_k(x) \le C(\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$. We also provide a counterexample to a theorem stated without proof by Lorentz (1963), who claimed that if some \phi_n \in \B_n satisfy $|f(x)-\phi_n(x)| \le C (\Delta_n(x))^\alpha$ for all $x \in [0,1]$ and $n \ge 1$, then $f \in C^\alpha [0,1]$.Comment: 29 pages; final version; to appear in Constructive Approximatio

Predicted effectiveness of daily and non-daily PrEP for MSM based on sex and pill-taking patterns from HPTN 067/ADAPT

Background: HPTN 067/ADAPT evaluated the feasibility of daily and non-daily HIV pre-exposure prophylaxis (PrEP) regimens among high-risk populations, including men who have sex with men (MSM) and transgender women, in Bangkok, Thailand and Harlem, New York, U.S. We used a mathematical model to predict the efficacy and effectiveness of different dosing regimens. Methods: An individual-based mathematical model was used to simulate annual HIV incidence among MSM cohorts. PrEP efficacy for covered sex acts, as defined in the HPTN 067/ADAPT protocol, was estimated using subgroup efficacy estimates from the iPrEx trial. Effectiveness was estimated by comparison of the HIV incidence with and without PrEP use. Results: We estimated that PrEP was highly protective (85%–96% efficacy across regimens and sites) for fully covered acts. PrEP was more protective for partially covered acts in Bangkok (71%–88% efficacy) than in Harlem (62%–81% efficacy). Our model projects 80%, 62%, and 68% effectiveness of daily, time-driven, and event-driven PrEP for MSM in Harlem compared with 90%, 85% and 79% for MSM in Bangkok. Halving the efficacy for partially covered acts decreases effectiveness by 8–9 percentage points in Harlem and by 5–9 percentage points in Bangkok across regimens. Conclusions: Our analysis suggests that PrEP was more effective among MSM in Thailand than in the U.S. as a result of more fully covered sex acts and more pills taken around partially covered acts. Overall, non-daily PrEP was less effective than daily PrEP, especially in the U.S. where the sex act coverage associated with daily use was substantially higher

Coupled Numerical Analysis of Variations in the Capacity of Driven Energy Piles in Clay

Energy piles are an emerging alternative for the reduction of energy consumption to heat and cool buildings. Most of the research to date has focused on thermodynamic properties or axial and radial stress and strain of piles. This paper focuses on the effects of temperature fluctuation on the capacity of driven energy piles in clayey soils. Consolidation of clay surrounding driven piles affects the pile capacity (i.e., set up in clay). The heating and cooling periods of energy piles can create the excess pore-water pressure (EPWP, ue) or relax the existing one (e.g., due to pile driving or previous thermal loads) in clayey soils (due to the contraction and expansion of water) affecting the pile capacity. In the meantime, the thermal expansion and contraction of the pile also generate or relax the EPWP in the soil, which can be computed using the cavity-expansion theory. This paper studies the resulting changes in the pile capacity due to the daily and seasonal thermal cycles. The results show that thermal cycles in an energy pile can cause a decrease in the pile capacity leading to a delay in reaching the capacity after a complete clay set up

Fast linear algebra is stable

In an earlier paper, we showed that a large class of fast recursive matrix multiplication algorithms is stable in a normwise sense, and that in fact if multiplication of $n$-by-$n$ matrices can be done by any algorithm in $O(n^{\omega + \eta})$ operations for any $\eta > 0$, then it can be done stably in $O(n^{\omega + \eta})$ operations for any $\eta > 0$. Here we extend this result to show that essentially all standard linear algebra operations, including LU decomposition, QR decomposition, linear equation solving, matrix inversion, solving least squares problems, (generalized) eigenvalue problems and the singular value decomposition can also be done stably (in a normwise sense) in $O(n^{\omega + \eta})$ operations.Comment: 26 pages; final version; to appear in Numerische Mathemati

Electron Accumulation and Emergent Magnetism in LaMnO3/SrTiO3 Heterostructures

Emergent phenomena at polar-nonpolar oxide interfaces have been studied intensely in pursuit of next-generation oxide electronics and spintronics. Here we report the disentanglement of critical thicknesses for electron reconstruction and the emergence of ferromagnetism in polar-mismatched LaMnO3/SrTiO3 (001) heterostructures. Using a combination of element-specific X-ray absorption spectroscopy and dichroism, and first-principles calculations, interfacial electron accumulation and ferromagnetism have been observed within the polar, antiferromagnetic insulator LaMnO3. Our results show that the critical thickness for the onset of electron accumulation is as thin as 2 unit cells (UC), significantly thinner than the observed critical thickness for ferromagnetism of 5 UC. The absence of ferromagnetism below 5 UC is likely induced by electron over-accumulation. In turn, by controlling the doping of the LaMnO3, we are able to neutralize the excessive electrons from the polar mismatch in ultrathin LaMnO3 films and thus enable ferromagnetism in films as thin as 3 UC, extending the limits of our ability to synthesize and tailor emergent phenomena at interfaces and demonstrating manipulation of the electronic and magnetic structures of materials at the shortest length scales.Comment: Accepted by Phys. Rev. Let