Mathematical Economics: A Reader

This paper is modeled as a hypothetical first lecture in a graduate Microeconomics or Mathematical Economics Course. We start with a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across Mathematical concepts and results that are used by economists. In the process we arrive at a classification of mathematical terms which is used to state mathematical results in economics. The usefulness of the classification scheme is illustrated with the help of a discussion of fixed-point theorems and Arrow's impossibility theorem. Several appendices provide a step-wise description of some mathematical concepts often used by economists and a few useful results in microeconomics.Mathematics, Set theory, Utility function, Arrow's impossibility theorem

The role of the Arabidopsis FUSCA3 transcription factor during inhibition of seed germination at high temperature

Abstract Background Imbibed seeds integrate environmental and endogenous signals to break dormancy and initiate growth under optimal conditions. Seed maturation plays an important role in determining the survival of germinating seeds, for example one of the roles of dormancy is to stagger germination to prevent mass growth under suboptimal conditions. The B3-domain transcription factor FUSCA3 (FUS3) is a master regulator of seed development and an important node in hormonal interaction networks in Arabidopsis thaliana. Its function has been mainly characterized during embryonic development, where FUS3 is highly expressed to promote seed maturation and dormancy by regulating ABA/GA levels. Results In this study, we present evidence for a role of FUS3 in delaying seed germination at supraoptimal temperatures that would be lethal for the developing seedlings. During seed imbibition at supraoptimal temperature, the FUS3 promoter is reactivated and induces de novo synthesis of FUS3 mRNA, followed by FUS3 protein accumulation. Genetic analysis shows that FUS3 contributes to the delay of seed germination at high temperature. Unlike WT, seeds overexpressing FUS3 (ML1:FUS3-GFP) during imbibition are hypersensitive to high temperature and do not germinate, however, they can fully germinate after recovery at control temperature reaching 90% seedling survival. ML1:FUS3-GFP hypersensitivity to high temperature can be partly recovered in the presence of fluridone, an inhibitor of ABA biosynthesis, suggesting this hypersensitivity is due in part to higher ABA level in this mutant. Transcriptomic analysis shows that WT seeds imbibed at supraoptimal temperature activate seed-specific genes and ABA biosynthetic and signaling genes, while inhibiting genes that promote germination and growth, such as GA biosynthetic and signaling genes. Conclusion In this study, we have uncovered a novel function for the master regulator of seed maturation, FUS3, in delaying germination at supraoptimal temperature. Physiologically, this is important since delaying germination has a protective role at high temperature. Transcriptomic analysis of seeds imbibed at supraoptimal temperature reveal that a complex program is in place, which involves not only the regulation of heat and dehydration response genes to adjust cellular functions, but also the activation of seed-specific programs and the inhibition of germination-promoting programs to delay germination

A Bi-Hamiltonian Structure for the Integrable, Discrete Non-Linear Schrodinger System

This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect to both a standard, local Poisson operator J and a new non-local, skew, almost Poisson operator K, on the appropriate space; (b) can be recursively generated from a recursion operator R (obtained by composing K and the inverse of J.) In addition, the proof of these facts relies upon two new pivotal resolvent identities which suggest a general method for uncovering bi-Hamiltonian structures for other families of discrete, integrable equations.Comment: 33 page

Planck Sunyaev-Zel'dovich Cluster Mass Calibration using Hyper Suprime-Cam Weak Lensing

Using $\sim$140 deg$^2$ Subaru Hyper Suprime-Cam (HSC) survey data, we stack the weak lensing (WL) signal around five Planck clusters found within the footprint. This yields a 15$\sigma$ detection of the mean Planck cluster mass density profile. The five Planck clusters span a relatively wide mass range, $M_{\rm WL,500c} = (2-30)\times10^{14}\,M_\odot/h$ with a mean mass of $M_{\rm WL,500c} = (4.15\pm0.61)\times10^{14}\,M_\odot/h$. The ratio of the stacked Planck Sunyaev-Zel'dovich (SZ) mass to the stacked WL mass is $\langle M_{\rm SZ}\rangle/\langle M_{\rm WL}\rangle = 1-b = 0.80\pm0.14$. This mass bias is consistent with previous WL mass calibrations of Planck clusters within the errors. We discuss the implications of our findings for the calibration of SZ cluster counts and the much discussed tension between Planck SZ cluster counts and Planck $\Lambda$CDM cosmology.Comment: 12 pages, 2 tables, 7 figures, accepted to PASJ special issu

Threat of deportation as proximal social determinant of mental health amongst migrant workers

Ministry of Education, Singapore under its Academic Research Funding Tier

Incorporating DNA Sequencing into Current Prenatal Screening Practice for Down's Syndrome

PMCID: PMC3604109This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

A practical implementation of the Overlap-Dirac operator

A practical implementation of the Overlap-Dirac operator ${{1+\gamma_5\epsilon(H)}\over 2}$ is presented. The implementation exploits the sparseness of $H$ and does not require full storage. A simple application to parity invariant three dimensional SU(2) gauge theory is carried out to establish that zero modes related to topology are exactly reproduced on the lattice.Comment: Y-axis label in figure correcte

Digital Signal Processing for Laser Printer Noise Source Detection and Identification

Presented here is the description of a software-based noise source detector that was developed to simplify the printing noise source identification process. The typical noise sources studied here were high frequency, stick-slip (squeaking) noises associated with rollers along the paper path. The detector was built by combining several digital signal processing procedures to first create a tone detector, and then to calculate the modulation spectrum of the tone. The latter is particularly important because it has been found that features appearing in the modulation spectrum can be directly associated with the rotational speed of various components in the printer; this allows the faulty part to be identified. By passing different printing noise samples through the detector, it was found that the detector accurately returned the acoustical characteristics of each noise sample, and then by matching those acoustical characteristics to the rotational speed of different parts, the detector was proven capable of providing robust and precise fault identification results