A number theoretic characterization of EE-smooth and (FRS) morphisms: estimates on the number of Z/pkZ\mathbb{Z}/p^{k}\mathbb{Z}-points

We provide uniform estimates on the number of $\mathbb{Z}/p^{k}\mathbb{Z}$-points lying on fibers of flat morphisms between smooth varieties whose fibers have rational singularities, termed (FRS) morphisms. For each individual fiber, the estimates were known by work of Avni and Aizenbud, but we render them uniform over all fibers. The proof technique for individual fibers is based on Hironaka's resolution of singularities and Denef's formula, but breaks down in the uniform case. Instead, we use recent results from the theory of motivic integration. Our estimates are moreover equivalent to the (FRS) property, just like in the absolute case by Avni and Aizenbud. In addition, we define new classes of morphisms, called $E$-smooth morphisms ($E\in\mathbb{N}$), which refine the (FRS) property, and use the methods we developed to provide uniform number-theoretic estimates as above for their fibers. Similar estimates are given for fibers of $\varepsilon$-jet flat morphisms, improving previous results by the last two authors.Comment: 27 pages, comments welcome; v2: the new notion of E-smooth morphisms was added, and uniform estimates on the number of points lying on the fibers of $E$-smooth and $\varepsilon$-jet flat morphisms are given (Theorems 4.11 and 4.12

Improvements on dimension growth results and effective Hilbert's irreducibility theorem

We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree $d$, over any global field. In particular, we focus on the the affine hypersurface situation by relaxing the condition on the top degree homogeneous part of the polynomial describing the affine hypersurface. Our work sharpens the dependence on the degree in the bounds, compared to~\cite{CCDN-dgc}. We also formulate a conjecture about plane curves which gives a conjectural approach to the uniform degree $3$ case (the only case which remains open). For induction on dimension, we develop a higher dimensional effective version of Hilbert's irreducibility theorem.Comment: 35 page

Nonlinear pricing of storable goods

This paper develops a model of nonlinear pricing of storable goods. We show that storability imposes novel constraints on a monopolist’s ability to extract surplus. We then show that the attempt to relax these constraints can generate cyclical patterns in pricing and sales, even when consumers are homogeneous. Thus, the model provides a novel explanation for sales that does not rely on discrimination motives. Enriching the model to allow for buyer heterogeneity in storage technology, delivers the prediction that larger containers are more likely to be on sale. This prediction is consistent with observed patterns in scanner data

Mode-coupling and nonlinear Landau damping effects in auroral Farley-Buneman turbulence

The fundamental problem of Farley-Buneman turbulence in the auroral $E$-region has been discussed and debated extensively in the past two decades. In the present paper we intend to clarify the different steps that the auroral $E$-region plasma has to undergo before reaching a steady state. The mode-coupling calculation, for Farley-Buneman turbulence, is developed in order to place it in perspective and to estimate its magnitude relative to the anomalous effects which arise through the nonlinear wave-particle interaction. This nonlinear effect, known as nonlinear ``Landau damping'' is due to the coupling of waves which produces other waves which in turn lose energy to the bulk of the particles by Landau damping. This leads to a decay of the wave energy and consequently a heating of the plasma. An equation governing the evolution of the field spectrum is derived and a physical interpration for each of its terms is provided

A comprehensive TALEN-based knockout library for generating human induced pluripotent stem cell-based models for cardiovascular diseases

Rationale: Targeted genetic engineering using programmable nucleases such as transcription activator-like effector nucleases (TALENs) is a valuable tool for precise, site-specific genetic modification in the human genome. Objective: The emergence of novel technologies such as human induced pluripotent stem cells (iPSCs) and nuclease-mediated genome editing represent a unique opportunity for studying cardiovascular diseases in vitro. Methods and Results: By incorporating extensive literature and database searches, we designed a collection of TALEN constructs to knockout (KO) eighty-eight human genes that are associated with cardiomyopathies and congenital heart diseases. The TALEN pairs were designed to induce double-strand DNA break near the starting codon of each gene that either disrupted the start codon or introduced a frameshift mutation in the early coding region, ensuring faithful gene KO. We observed that all the constructs were active and disrupted the target locus at high frequencies. To illustrate the general utility of the TALEN-mediated KO technique, six individual genes (TNNT2, LMNA/C, TBX5, MYH7, ANKRD1, and NKX2.5) were knocked out with high efficiency and specificity in human iPSCs. By selectively targeting a dilated cardiomyopathy (DCM)-causing mutation (TNNT2 p.R173W) in patient-specific iPSC-derived cardiac myocytes (iPSC-CMs), we demonstrated that the KO strategy ameliorates the DCM phenotype in vitro. In addition, we modeled the Holt-Oram syndrome (HOS) in iPSC-CMs in vitro and uncovered novel pathways regulated by TBX5 in human cardiac myocyte development. Conclusions: Collectively, our study illustrates the powerful combination of iPSCs and genome editing technology for understanding the biological function of genes and the pathological significance of genetic variants in human cardiovascular diseases. The methods, strategies, constructs and iPSC lines developed in this study provide a validated, readily available resource for cardiovascular research