Weighted bounds for variational Fourier series

For 1<p<infty and for weight w in A_p, we show that the r-variation of the Fourier sums of any function in L^p(w) is finite a.e. for r larger than a finite constant depending on w and p. The fact that the variation exponent depends on w is necessary. This strengthens previous work of Hunt-Young and is a weighted extension of a variational Carleson theorem of Oberlin-Seeger-Tao-Thiele-Wright. The proof uses weighted adaptation of phase plane analysis and a weighted extension of a variational inequality of Lepingle.Comment: 31 pages. v2: Minor changes. To appear in Studia Mat

On the Convergence of Lacunary Walsh-Fourier Series

We study the Walsh-Fourier series of S_{n_j}f, along a lacunary subsequence of integers {n_j}. Under a suitable integrability condition, we show that the sequence converges to f a.e. Integral condition is only slightly larger than what the sharp integrability condition would be, by a result of Konyagin. The condition is: f is in L loglog L (logloglog L). The method of proof uses four ingredients, (1) analysis on the Walsh Phase Plane, (2) the new multi-frequency Calderon-Zygmund Decomposition of Nazarov-Oberlin-Thiele, (3) a classical inequality of Zygmund, giving an improvement in the Hausdorff-Young inequality for lacunary subsequences of integers, and (4) the extrapolation method of Carro-Martin, which generalizes the work of Antonov and Arias-de-Reyna.Comment: 18 pages. v2: Several typos corrected. Final version of the paper, accepted to LM

Signatures of Energy Flux in Particle Production: A Black Hole Birth Cry and Death Gasp

It is recently argued that if the Hawking radiation process is unitary, then a black hole's mass cannot be monotonically decreasing. We examine the time dependent particle count and negative energy flux in the non-trivial conformal vacuum via the moving mirror approach. A new, exactly unitary solution is presented which emits a characteristic above-thermal positive energy burst, a thermal plateau, and negative energy flux. It is found that the characteristic positive energy flare and thermal plateau is observed in the particle outflow. However, the results of time dependent particle production show no overt indication of negative energy flux. Therefore, a black hole's birth cry is detectable by asymptotic observers via particle count, whereas its death gasp is not.Comment: 12 pages, 6 figure

Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, using Sparse Linear Programming

We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at baseline. The goal is to simultaneously learn which subpopulations benefit from an experimental treatment, while providing strong control of the familywise Type I error rate. We formalize this as a multiple testing problem and show it is computationally infeasible to solve using existing techniques. Our solution involves a novel approach, in which we first transform the original multiple testing problem into a large, sparse linear program. We then solve this problem using advanced optimization techniques. This general method can solve a variety of multiple testing problems and decision theory problems related to optimal trial design, for which no solution was previously available. In particular, we construct new multiple testing procedures that satisfy minimax and Bayes optimality criteria. For a given optimality criterion, our new approach yields the optimal tradeoff? between power to detect an effect in the overall population versus power to detect effects in subpopulations. We demonstrate our approach in examples motivated by two randomized trials of new treatments for HIV

OR15-5 Human Sex Determination at the Edge of Ambiguity: Impaired SRY Phosphorylation Attenuates Expression of the Male Program

A paradox is posed by metazoan gene-regulatory networks (GRNs) that are robust yet evolvable. Insight may be obtained through studies of bistable genetic circuits mediating developmental decisions. A model in organogenesis is provided by the sex-specific differentiation of the embryonic gonadal ridge to form a testis or ovary. Here, we investigated a Swyer mutation in human testis-determining factor SRY that impairs its phosphorylation in association with variable developmental outcomes: fertile male, intersex, or infertile female (46, XY pure gonadal dysgenesis). The mutation (R30I) abrogates serine phosphorylation within a putative target site for protein kinase A (PKA) N-terminal to the HMG box. Diverse processes can be regulated by protein phosphorylation, including DNA recognition by transcription factors (TFs). Phosphorylation of this site in human SRY (LRRSSSFLCT; italics) in vitro was previously shown to enhance specific DNA affinity. Biological consequences of the mutation were evaluated in SRY-responsive mammalian cell lines following transient transfection. The mutation attenuated in concert occupancy of a target enhancer (TESCO) and SOX9 transcriptional activation. These perturbations were mitigated by acidic substitution (LRIDDDFL) whereas Ala substitutions (RRAAAFL or RIAAAFL) attenuated activity to an extent similar to R30I alone. No differences were observed in nuclear localization. Mutagenesis suggested that the central Ser is most efficiently phosphorylated in accord with PKA targeting rules. Replacement of the native site by an optimized “Kemptide” PKA site (LRRASLGCT) enhanced both SRY phosphorylation and SOX9 transcriptional activation whereas a “swapped” protein-kinase C determinant (LRRSSFRRCT) blocked phosphorylation. Among SRY variants, extent of cellular phosphorylation mirrored relative in vitro efficiencies of synthetic SRY-derived peptides as PKA-specific substrates. Although several kinases are predicted in silico to target this tri-serine motif, cell-based studies implicate PKA as the relevant kinase in vivo. Our results provide evidence that primate Sry requires its phosphorylation for full gene-regulatory activity. A PKA site N-terminal to the SRY HMG box, unique to primates, exemplifies network “tinkering” through recruitment of a new regulatory linkage. Molecular characterization of the R30I inherited Swyer mutation in SRY thus demonstrates that impaired TF phosphorylation can attenuate a human developmental switch at the edge of ambiguity

Tunable current circulation in triangular quantum-dot metastructures

Advances in fabrication and control of quantum dots allow the realization of metastructures that may exhibit novel electrical transport phenomena. Here, we investigate the electrical current passing through one such metastructure, a system composed of quantum dots placed at the vertices of a triangle. The wave natural of quantum particles leads to internal current circulation within the metastructure in the absence of any external magnetic field. We uncover the relation between its steady-state total current and the internal circulation. By calculating the electronic correlations in quantum transport exactly, we present phase diagrams showing where different types of current circulation can be found as a function of the correlation strength and the coupling between the quantum dots. Finally, we show that the regimes of current circulation can be further enhanced or reduced depending on the local spatial distribution of the interactions, suggesting a single-particle scattering mechanism is at play even in the strongly-correlated regime. We suggest experimental realizations of actual quantum-dot metastructures where our predictions can be directly tested.Comment: 5 pages, 4 figures, the Supplemental Information is attached at the en

Giant Tortoise Coordinate

The giant tortoise coordinate is a moving mirror inspired generalization of the Regge-Wheeler counterpart that demonstrates a unitary evaporating black hole emitting a total finite energy.Comment: 10 pages, 1 figur