Pseudofinite proofs of the stable graph regularity lemma

This expository article is based on two lectures given by the first author at the Fields Institute in the Fall 2021 Thematic Program on Trends in Pure and Applied Model Theory. We give a detailed proof of a qualitative version of the Mallaris-Shelah regularity lemma for stable graphs using only basic local stability theory and an ultraproduct construction. This proof strategy was first established by Malliaris and Pillay, and later simplified by Pillay. We provide some further simplifications, and also explain how the pseudofinite approach can be used to obtain a qualitative strengthening (compared to previous proofs) in terms of "functional error". To illustrate the extra leverage obtained by functional error, we give an elementary argument for extracting equipartitions from arbitrary partitions.Comment: 15 pages, submitted as a chapter in a forthcoming title of the Fields Institute Monographs book serie

Hybrid computer Monte-Carlo techniques

Hybrid analog-digital computer systems for Monte Carlo method application

Nonrandom Survival of Gene Conversions among Yeast Ribosomal Proteins Duplicated through Genome Doubling

By comparing the patterns of evolution in the coding and upstream noncoding regions of yeast ribosomal protein (RP) genes duplicated in a genome duplication, we find that although nonsynonymous sites in the coding sequences show strong evidence for the fixation of recent gene conversion events, similar patterns are less evident among the synonymous positions and noncoding regulatory elements. This result suggests a potential explanation for the somewhat puzzling fact that duplicated RP genes are not functionally redundant despite their very high protein sequence identity. An analysis of the patterns of regulatory network evolution after genome duplication also indicates that the duplicated proteins have diverged considerably in expression despite their similar protein sequences

Symbols in Wittgenstein's Tractatus

This paper is concerned with the status of a symbol in Wittgenstein’s Tractatus. It is claimed in the first section that a Tractarian symbol, whilst essentially a syntactic entity to be distinguished from the mark or sound that is its sign, bears its semantic significance only inessentially. In the second and third sections I pursue this point of exegesis through the Tractarian discussions of nonsense and the context principle respectively. The final section of the paper places the forgoing work in a secondary context, addressing in particular a debate regarding the realism of the Tractatus

Intratumoral T-cell receptor repertoire composition predicts overall survival in patients with pancreatic ductal adenocarcinoma

Pancreatic ductal adenocarcinoma (PDAC) is a lethal malignancy that is refractory to immune checkpoint inhibitor therapy. However, intratumoral T-cell infiltration correlates with improved overall survival (OS). Herein, we characterized the diversity and antigen specificity of the PDAC T-cell receptor (TCR) repertoire to identify novel immune-relevant biomarkers. Demographic, clinical, and TCR-beta sequencing data were collated from 353 patients across three cohorts that underwent surgical resection for PDAC. TCR diversity was calculated using Shannon Wiener index, Inverse Simpson index, and True entropy. Patients were clustered by shared repertoire specificity. TCRs predictive of OS were identified and their associated transcriptional states were characterized by single-cell RNAseq. In multivariate Cox regression models controlling for relevant covariates, high intratumoral TCR diversity predicted OS across multiple cohorts. Conversely, in peripheral blood, high abundance of T-cells, but not high diversity, predicted OS. Clustering patients based on TCR specificity revealed a subset of TCRs that predicts OS. Interestingly, these TCR sequences were more likely to encode CD

Stable Optical Phase Modulation with Micromirrors

We measure the motional fluctuations of a micromechanical mirror using a Michelson interferometer, and demonstrate its interferometric stability. The position stability of the micromirror is dominated by the thermal mechanical noise of the structure. With this level of stability, we utilize the micromirror to realize an ideal optical phase modulator by simply reflecting light off the mirror and modulating its position. The resonant frequency of the modulator can be tuned by applying a voltage between the mirror and an underlying electrode. Full modulation depth of +/-\pi is achieved when the mirror resonantly excited with a sinusoidal voltage at an amplitude of 11V.Comment: 4 pages, 3 figure

Synergistic effects of the invasive Chinese tallow (Triadica sebifera) and climate change on aquatic amphibian survival

Changes in climate and the introduction of invasive species are two major stressors to amphibians, although little is known about the interaction between these two factors with regard to impacts on amphibians. We focused our study on an invasive tree species, the Chinese tallow (Triadica sebifera), that annually sheds its leaves and produces leaf litter that is known to negatively impact aquatic amphibian survival. The purpose of our research was to determine whether the timing of leaf fall from Chinese tallow and the timing of amphibian breeding (determined by weather) influence survival of amphibian larvae. We simulated a range of winter weather scenarios, ranging from cold to warm, by altering the relative timing of when leaf litter and amphibian larvae were introduced into aquatic mesocosms. Our results indicate that amphibian larvae survival was greatly affected by the length of time Chinese tallow leaf litter decomposes in water prior to the introduction of the larvae. Larvae in treatments simulating warm winters (early amphibian breeding) were introduced to the mesocosms early in the aquatic decomposition process of the leaf litter and had significantly lower survival compared with cold winters (late amphibian breeding), likely due to significantly lower dissolved oxygen levels. Shifts to earlier breeding phenology, linked to warming climate, have already been observed in many amphibian taxa, and with most climate models predicting a significant warming trend over the next century, the trend toward earlier breeding should continue if not increase. Our results strongly suggest that a warming climate can interact with the effects of invasive plant species, in ways we have not previously considered, to reduce the survival of an already declining group of organisms

LPMLE3 : a novel 1-D approach to study water flow in streambeds using heat as a tracer

We introduce LPMLE3, a new 1-D approach to quantify vertical water flow components at streambeds using temperature data collected in different depths. LPMLE3 solves the partial differential equation for coupled water flow and heat transport in the frequency domain. Unlike other 1-D approaches it does not assume a semi-infinite halfspace with the location of the lower boundary condition approaching infinity. Instead, it uses local upper and lower boundary conditions. As such, the streambed can be divided into finite subdomains bound at the top and bottom by a temperature-time series. Information from a third temperature sensor within each subdomain is then used for parameter estimation. LPMLE3 applies a low order local polynomial to separate periodic and transient parts (including the noise contributions) of a temperature-time series and calculates the frequency response of each subdomain to a known temperature input at the streambed top. A maximum-likelihood estimator is used to estimate the vertical component of water flow, thermal diffusivity, and their uncertainties for each streambed subdomain and provides information regarding model quality. We tested the method on synthetic temperature data generated with the numerical model STRIVE and demonstrate how the vertical flow component can be quantified for field data collected in a Belgian stream. We show that by using the results in additional analyses, nonvertical flow components could be identified and by making certain assumptions they could be quantified for each subdomain. LPMLE3 performed well on both simulated and field data and can be considered a valuable addition to the existing 1-D methods