Contracting Endomorphisms of Valued Fields

We prove that the class of separably algebraically closed valued fields equipped with a distinguished Frobenius endomorphism $x \mapsto x^q$ is decidable, uniformly in $q$. The result is a simultaneous generalization of the work of Chatzidakis and Hrushovski (in the case of the trivial valuation) and the work of the first author and Hrushovski (in the case where the fields are algebraically closed). The logical setting for the proof is a model completeness result for valued fields equipped with an endomorphism $\sigma$ which is locally infinitely contracting and fails to be onto. Namely we prove the existence of a model complete theory $\widetilde{\mathrm{VFE}}$ amalgamating the theories $\mathrm{SCFE}$ and $\widetilde{\mathrm{VFA}}$ introduced in [4] and [9], respectively. In characteristic zero, we also prove that $\widetilde{\mathrm{VFE}}$ is NTP$_2$ and classify the stationary types: they are precisely those orthogonal to the fixed field and the valuation group

Specialization of Difference Equations and High Frobenius Powers

We study valued fields equipped with an automorphism $\sigma$ which is locally infinitely contracting in the sense that $\alpha\ll\sigma\alpha$ for all $0<\alpha\in\Gamma$. We show that various notions of valuation theory, such as Henselian and strictly Henselian hulls, admit meaningful transformal analogues. We prove canonical amalgamation results, and exhibit the way that transformal wild ramification is controlled by torsors over generalized vector groups. Model theoretically, we determine the model companion: it is decidable, admits a simple axiomatization, and enjoys elimination of quantifiers up to algebraically bounded quantifiers. The model companion is shown to agree with the limit theory of the Frobenius action on an algebraically closed and nontrivially valued field. This opens the way to a motivic intersection theory for difference varieties that was previously available only in characteristic zero. As a first consequence, the class of algebraically closed valued fields equipped with a distinguished Frobenius $x\mapsto x^{q}$ is decidable, uniformly in $q$.Comment: identical to v1 apart from slight modifications in abstrac

Towards a User Privacy-Aware Mobile Gaming App Installation Prediction Model

Over the past decade, programmatic advertising has received a great deal of attention in the online advertising industry. A real-time bidding (RTB) system is rapidly becoming the most popular method to buy and sell online advertising impressions. Within the RTB system, demand-side platforms (DSP) aim to spend advertisers' campaign budgets efficiently while maximizing profit, seeking impressions that result in high user responses, such as clicks or installs. In the current study, we investigate the process of predicting a mobile gaming app installation from the point of view of a particular DSP, while paying attention to user privacy, and exploring the trade-off between privacy preservation and model performance. There are multiple levels of potential threats to user privacy, depending on the privacy leaks associated with the data-sharing process, such as data transformation or de-anonymization. To address these concerns, privacy-preserving techniques were proposed, such as cryptographic approaches, for training privacy-aware machine-learning models. However, the ability to train a mobile gaming app installation prediction model without using user-level data, can prevent these threats and protect the users' privacy, even though the model's ability to predict may be impaired. Additionally, current laws might force companies to declare that they are collecting data, and might even give the user the option to opt out of such data collection, which might threaten companies' business models in digital advertising, which are dependent on the collection and use of user-level data. We conclude that privacy-aware models might still preserve significant capabilities, enabling companies to make better decisions, dependent on the privacy-efficacy trade-off utility function of each case.Comment: 11 pages, 3 figure

Approximate polymorphisms

For a function g¶{0,1}m→{0,1}, a function f¶ {0,1}n→{0,1} is called a g-polymorphism if their actions commute: f(g(row1(Z)) g(rown(Z))) = g(f(col1(Z)) f(colm(Z))) for all Z{0,1}n× m. The function f is called an approximate g-polymorphism if this equality holds with probability close to 1, when Z is sampled uniformly. A pair of functions f0,f1¶ {0,1}n → {0,1} are called a skew g-polymorphism if f0(g(row1(Z)) g(rown(Z))) = g(f1(col1(Z)) f1(colm(Z))) for all Z{0,1}n× m. We study the structure of exact polymorphisms as well as approximate polymorphisms. Our results include a proof that an approximate polymorphism f must be close to an exact skew polymorphism, and a characterization of exact skew polymorphisms, which shows that besides trivial cases, only the functions AND, XOR, OR, NAND, NOR, XNOR admit non-trivial exact skew polymorphisms. We also study the approximate polymorphism problem in the list-decoding regime (i.e., when the probability equality holds is not close to 1, but is bounded away from some value). We show that if f(x § y) = f(x) § f(y) with probability larger than s§≈ 0.815 then f correlates with some junta, and s§ is the optimal threshold for this property. Our result generalize the classical linearity testing result of Blum, Luby and Rubinfeld, that in this language showed that the approximate polymorphisms of g = XOR are close to XOR's, as well as a recent result of Filmus, Lifshitz, Minzer and Mossel, showing that the approximate polymorphisms of AND can only be close to AND functions. © 2022 Owner/Author

Loss of Liver Kinase B1 (LKB1) in Beta Cells Enhances Glucose-stimulated Insulin Secretion Despite Profound Mitochondrial Defects

The tumor suppressor liver kinase B1 (LKB1) is an important regulator of pancreatic β cell biology. LKB1-dependent phosphorylation of distinct AMPK (adenosine monophosphate-activated protein kinase) family members determines proper β cell polarity and restricts β cell size, total β cell mass, and glucose-stimulated insulin secretion (GSIS). However, the full spectrum of LKB1 effects and the mechanisms involved in the secretory phenotype remain incompletely understood. We report here that in the absence of LKB1 in β cells, GSIS is dramatically and persistently improved. The enhancement is seen both in vivo and in vitro and cannot be explained by altered cell polarity, increased β cell number, or increased insulin content. Increased secretion does require membrane depolarization and calcium influx but appears to rely mostly on a distal step in the secretion pathway. Surprisingly, enhanced GSIS is seen despite profound defects in mitochondrial structure and function in LKB1-deficient β cells, expected to greatly diminish insulin secretion via the classic triggering pathway. Thus LKB1 is essential for mitochondrial homeostasis in β cells and in parallel is a powerful negative regulator of insulin secretion. This study shows that β cells can be manipulated to enhance GSIS to supra-normal levels even in the face of defective mitochondria and without deterioration over months

CEL-Seq2: sensitive highly-multiplexed single-cell RNA-Seq

Single-cell transcriptomics requires a method that is sensitive, accurate, and reproducible. Here, we present CEL-Seq2, a modified version of our CEL-Seq method, with threefold higher sensitivity, lower costs, and less hands-on time. We implemented CEL-Seq2 on Fluidigm’s C1 system, providing its first single-cell, on-chip barcoding method, and we detected gene expression changes accompanying the progression through the cell cycle in mouse fibroblast cells. We also compare with Smart-Seq to demonstrate CEL-Seq2’s increased sensitivity relative to other available methods. Collectively, the improvements make CEL-Seq2 uniquely suited to single-cell RNA-Seq analysis in terms of economics, resolution, and ease of use.Seventh Framework Programme (European Commission)Israel Science Foundatio

Dysregulation of Dicer1 in Beta Cells Impairs Islet Architecture and Glucose Metabolism

microRNAs (miRNAs) play important roles in pancreas development and in regulation of insulin expression in the adult. Here we show that loss of miRNAs activity in beta-cells during embryonic development results in lower beta-cell mass and in impaired glucose tolerance. Dicer1-null cells initially constitute a significant portion of the total beta-cell population. However, during postnatal development, Dicer1-null cells are depleted. Furthermore, wild-type beta cells are repopulating the islets in complex compensatory dynamics. Because loss of Dicer1 is also associated with changes in the distribution of membranous E-cadherin, we hypothesized that E-cadherin activity may play a role in beta cell survival or islet architecture. However, genetic loss of E-cadherin function does not impair islet architecture, suggesting that miRNAs likely function through other or redundant effectors in the endocrine pancreas

Gastrin: A Distinct Fate of Neurogenin3 Positive Progenitor Cells in the Embryonic Pancreas

Neurogenin3+ (Ngn3+) progenitor cells in the developing pancreas give rise to five endocrine cell types secreting insulin, glucagon, somatostatin, pancreatic polypeptide and ghrelin. Gastrin is a hormone produced primarily by G-cells in the stomach, where it functions to stimulate acid secretion by gastric parietal cells. Gastrin is expressed in the embryonic pancreas and is common in islet cell tumors, but the lineage and regulators of pancreatic gastrin+ cells are not known. We report that gastrin is abundantly expressed in the embryonic pancreas and disappears soon after birth. Some gastrin+ cells in the developing pancreas co-express glucagon, ghrelin or pancreatic polypeptide, but many gastrin+ cells do not express any other islet hormone. Pancreatic gastrin+ cells express the transcription factors Nkx6.1, Nkx2.2 and low levels of Pdx1, and derive from Ngn3+ endocrine progenitor cells as shown by genetic lineage tracing. Using mice deficient for key transcription factors we show that gastrin expression depends on Ngn3, Nkx2.2, NeuroD1 and Arx, but not Pax4 or Pax6. Finally, gastrin expression is induced upon differentiation of human embryonic stem cells to pancreatic endocrine cells expressing insulin. Thus, gastrin+ cells are a distinct endocrine cell type in the pancreas and an alternative fate of Ngn3+ cells