A note on Elkin's improvement of Behrend's construction

We provide a short proof of a recent result of Elkin in which large subsets of the integers 1 up to N free of 3-term progressions are constructed.Comment: 4 pages, submitted to volume in honour of Mel Nathanso

The potential of combining MATISSE and ALMA observations: Constraining the structure of the innermost region in protoplanetary discs

In order to study the initial conditions of planet formation, it is crucial to obtain spatially resolved multi-wavelength observations of the innermost region of protoplanetary discs. We evaluate the advantage of combining observations with MATISSE/VLTI and ALMA to constrain the radial and vertical structure of the dust in the innermost region of circumstellar discs in nearby star-forming regions. Based on a disc model with a parameterized dust density distribution, we apply 3D radiative-transfer simulations to obtain ideal intensity maps. These are used to derive the corresponding wavelength-dependent visibilities we would obtain with MATISSE as well as ALMA maps simulated with CASA. Within the considered parameter space, we find that constraining the dust density structure in the innermost $5\,$au around the central star is challenging with MATISSE alone, whereas ALMA observations with reasonable integration times allow us to derive significant constraints on the disc surface density. However, we find that the estimation of the different disc parameters can be considerably improved by combining MATISSE and ALMA observations. For example, combining a 30-minute ALMA observation (at 310 GHz with an angular resolution of 0.03$^{\prime\prime}$) for MATISSE observations in the L and M bands (with visibility accuracies of about $3\,\%$) allows the radial density slope and the dust surface density profile to be constrained to within $\Delta \alpha=0.3$ and $\Delta (\alpha-\beta)=0.15$, respectively. For an accuracy of ${\sim 1\%}$ even the disc flaring can be constrained to within $\Delta \beta=0.1$. To constrain the scale height to within $5\,$au, M band accuracies of $0.8\,\%$ are required. While ALMA is sensitive to the number of large dust grains settled to the disc midplane we find that the impact of the surface density distribution of the large grains on the observed quantities is small.Comment: 12 pages, 12 figures, 1 table, accepted by A&

Quantum Communication Cannot Simulate a Public Coin

We study the simultaneous message passing model of communication complexity. Building on the quantum fingerprinting protocol of Buhrman et al., Yao recently showed that a large class of efficient classical public-coin protocols can be turned into efficient quantum protocols without public coin. This raises the question whether this can be done always, i.e. whether quantum communication can always replace a public coin in the SMP model. We answer this question in the negative, exhibiting a communication problem where classical communication with public coin is exponentially more efficient than quantum communication. Together with a separation in the other direction due to Bar-Yossef et al., this shows that the quantum SMP model is incomparable with the classical public-coin SMP model. In addition we give a characterization of the power of quantum fingerprinting by means of a connection to geometrical tools from machine learning, a quadratic improvement of Yao's simulation, and a nearly tight analysis of the Hamming distance problem from Yao's paper.Comment: 12 pages LaTe

Strengths and Weaknesses of Quantum Fingerprinting

We study the power of quantum fingerprints in the simultaneous message passing (SMP) setting of communication complexity. Yao recently showed how to simulate, with exponential overhead, classical shared-randomness SMP protocols by means of quantum SMP protocols without shared randomness ($Q^\parallel$-protocols). Our first result is to extend Yao's simulation to the strongest possible model: every many-round quantum protocol with unlimited shared entanglement can be simulated, with exponential overhead, by $Q^\parallel$-protocols. We apply our technique to obtain an efficient $Q^\parallel$-protocol for a function which cannot be efficiently solved through more restricted simulations. Second, we tightly characterize the power of the quantum fingerprinting technique by making a connection to arrangements of homogeneous halfspaces with maximal margin. These arrangements have been well studied in computational learning theory, and we use some strong results obtained in this area to exhibit weaknesses of quantum fingerprinting. In particular, this implies that for almost all functions, quantum fingerprinting protocols are exponentially worse than classical deterministic SMP protocols.Comment: 13 pages, no figures, to appear in CCC'0

Exponential Separation of Quantum and Classical One-Way Communication Complexity for a Boolean Function

We give an exponential separation between one-way quantum and classical communication complexity for a Boolean function. Earlier such a separation was known only for a relation. A very similar result was obtained earlier but independently by Kerenidis and Raz [KR06]. Our version of the result gives an example in the bounded storage model of cryptography, where the key is secure if the adversary has a certain amount of classical storage, but is completely insecure if he has a similar amount of quantum storage.Comment: 8 pages, no figure

Localization-dependent charge separation efficiency at an organic/inorganic hybrid interface

By combining complementary optical techniques, photoluminescence and time-resolved excited state absorption, we achieve a comprehensive picture of the relaxation processes in the organic/inorganic hybrid system SP6/ZnO. We identify two long-lived excited states of the organic molecules of which only the lowest energy one, localized on the sexiphenyl backbone of the molecule, is found to efficiently charge separate to the ZnO conduction band or radiatively recombine. The other state, most likely localized on the spiro-linked biphenyl, relaxes only by intersystem crossing to a long-lived, probably triplet state, thus acting as a sink of the excitation and limiting the charge separation efficiency.Comment: 6 pages, 5 figure

Sampling-based proofs of almost-periodicity results and algorithmic applications

We give new combinatorial proofs of known almost-periodicity results for sumsets of sets with small doubling in the spirit of Croot and Sisask, whose almost-periodicity lemma has had far-reaching implications in additive combinatorics. We provide an alternative (and L^p-norm free) point of view, which allows for proofs to easily be converted to probabilistic algorithms that decide membership in almost-periodic sumsets of dense subsets of F_2^n. As an application, we give a new algorithmic version of the quasipolynomial Bogolyubov-Ruzsa lemma recently proved by Sanders. Together with the results by the last two authors, this implies an algorithmic version of the quadratic Goldreich-Levin theorem in which the number of terms in the quadratic Fourier decomposition of a given function is quasipolynomial in the error parameter, compared with an exponential dependence previously proved by the authors. It also improves the running time of the algorithm to have quasipolynomial dependence instead of an exponential one. We also give an application to the problem of finding large subspaces in sumsets of dense sets. Green showed that the sumset of a dense subset of F_2^n contains a large subspace. Using Fourier analytic methods, Sanders proved that such a subspace must have dimension bounded below by a constant times the density times n. We provide an alternative (and L^p norm-free) proof of a comparable bound, which is analogous to a recent result of Croot, Laba and Sisask in the integers.Comment: 28 page

A Review of Dreamland: The true tale of America's opiate epidemic by Sam Quinones

No abstract available

Health Disparities by Sexual Orientation Components in the United States

Fundamental cause theory encourages researchers to consider broad social conditions that put people at risk of individual-level health-related risks that can lead to health disparities between social groups. Stigma has recently been proposed as a fundamental cause of health disparities as it influences multiple disease outcomes, affects access to resources, and is consistently related to health inequities across historical and geographical contexts. Minority stress theory describes how sexual minorities endure excess stressors in the form of prejudice and discrimination due to their stigmatized status. Considering both frameworks, I explore how stigmatized sexual orientation minority respondents compare to their sexual majority counterparts on a holistic subjective measure of health, an objective measure of health, and a measure regarding access to health care. Sexual minority health research has grown rapidly in recent years, but data and methodology limitations have restricted analyses and subsequent topic knowledge at a national level. Using nine years of nationally representative data from the National Survey of Family Growth (NSFG; 2011-2019), I explore three health-related variables—self-rated health (SRH), body mass index (BMI), and access to a usual source of health care (USOC)—by three components of sexual orientation—sexual orientation identity, sexual attraction, and sexual behavior. I provide summary statistics on these elements and other demographic and socioeconomic factors as well as report logistic and multinomial regression results on the health-related variables by each sexual orientation component. Chapter one analyzes the entire NSFG sample except for respondents who were pregnant, under age 25, and/or were missing responses for any variables used (N=23,567). Chapter two splits the qualified sample into females (N=12,895) and males (N=10,672) and Chapter three splits the qualified sample into two age groups (25-34 years old, N=13,038; 35-44 years old, N=10,529)—both report the results of the same analyses on the split samples. Only one result was consistently found across chapters—those who have had sexual experiences with someone of the same sex have lower odds of reporting excellent, very good, or good SRH compared to those who have had no same-sex sexual experience. All other significant differences vary by group analyzed; the male sample had the highest number of significant differences in health outcomes by sexual orientation components and the 35-44 age group sample had the least number of significant differences. We must use an intersectional perspective that considers other statuses such as sex and age to properly investigate and address health-related issues for sexual orientation minorities