Large Discrepancy In Homogenous Quasi-Arithmetic Progressions

We prove that the class of homogeneous quasi-arithmetic progressions has unbounded discrepancy. That is, we show that given any 2-coloring of the natural numbers and any positive integer D, one can find a real number α≥1 and a set of natural numbers of the form {0, [α], [2α], [3α], . . . , [kα]} so that one color appears at least D times more than the other color. This was already proved by Beck in 1983, but the proof given here is somewhat simpler and gives a better bound on the discrepancy.     

Sensitivity and specificity of the BAX for screening/Listeria monocytogenes assay: internal validation and independent laboratory study

In this study to certify the BAX for Screening/Listeria monocytogenes assay (DuPont Qualicon, Wilmington, DE), an internal evaluation was conducted on 16 food types that were simultaneously analyzed with the BAX system (BAX), and the ISO method for the detection of L. monocytogenes (ISO). No statistically significant difference in performance between the BAX and ISO methods was observed. Inclusivity/exclusivity testing showed that the BAX system was able to detect 97 of 97 (100%) of L. monocytogenes strains tested. None of 56 other Listeria species or non-Listeria tested gave a reproducible positive BAX result. Ruggedness testing demonstrated that performance of the assay was not affected by reasonable variability in the operating parameters. BAX was then submitted for independent laboratory validation. In this phase, BAX was compared with standard culture methods for the detection of L. monocytogenes in chicken (USDA-FSIS), crab meat (BAM), and milk (AOAC). This study validated product claims of sensitivity and specificity >98% in accordance with AOAC Performance Tested Method requirements.     

The Coordinate Reaction Model: An Obstacle to Interpreting the Emergence of Chemical Complexity

The way chemical transformations are described by models based on microscopic reversibility does not take into account the irreversibility of natural processes, and therefore, in complex chemical networks working in open systems, misunderstandings may arise about the origin and causes of the stability of non-equilibrium stationary states, and general constraints on evolution in systems that are far from equilibrium. In order to be correctly simulated and understood, the chemical behavior of complex systems requires time-dependent models, otherwise the irreversibility of natural phenomena is overlooked. Micro reversible models based on the reaction-coordinate model are time invariant and are therefore unable to explain the evolution of open dissipative systems. The important points necessary for improving the modeling and simulations of complex chemical systems are: a) understanding the physical potential related to the entropy production rate, which is in general an inexact differential of a state function, and b) the interpretation and application of the so-called general evolution criterion (GEC), which is the general thermodynamic constraint for the evolution of dissipative chemical systems.     

The galaxy-galaxy correlation function as an indicator of critical phenomena in cosmology

We approximate the observable Universe by a collection of equal mass galaxies linked into a many body system by their mutual gravitational interaction. Under the assumptions of (i) nonrelativistic approximation and (ii) global quasi-equilibrium, the partition function of this system can be cast in terms of Ising model spin variables and maps exactly onto a three-dimensional scalar classical field theory. The full machinery of the renormalization group and critical phenomena is brought to bear on this field theory allowing one to calculate the galaxy-to-galaxy correlation function, whose critical exponent is predicted to be between 1.530 to 1.862, to be compared to the phenomenological/observational value of 1.6 to 1.8.     

Multiplexed inkjet functionalization of silicon photonic biosensors

The transformative potential of silicon photonics for chip-scale biosensing is limited primarily by the inability to selectively functionalize and exploit the extraordinary density of integrated optical devices on this platform. Silicon biosensors, such as the microring resonator, can be routinely fabricated to occupy a footprint of less than 50 × 50 μm; however, chemically addressing individual devices has proven to be a significant challenge due to their small size and alignment requirements. Herein, we describe a non-contact piezoelectric (inkjet) method for the rapid and efficient printing of bioactive proteins, glycoproteins and neoglycoconjugates onto a high-density silicon microring resonator biosensor array. This approach demonstrates the scalable fabrication of multiplexed silicon photonic biosensors for lab-on-a-chip applications, and is further applicable to the functionalization of any semiconductor-based biosensor chip.     

Gravitational critical phenomena in the realm of the galaxies and Ising magnets

In the non-relativistic and quasi-static limit, it is possible to map exactly the system of galaxies in the observable universe onto an Ising magnet. Techniques from the theory of critical phenomena as applied to magnets can then be employed to calculate rigorously the galaxy-to-galaxy correlation function, whose critical exponent is predicted to be between 1.530 to 1.862, to be compared to the empirical/observational value of 1.6 to 1.8.This essay received the fifth award from the Gravity Research Foundation, 1996—Ed.     

Confidence Interval for the Risk-Score Index

Risk-score indices are a simple, applicable, and easy-to-calculate tool for regression models, which can be used when computers are not available. The risk-score index is a partial summation of the rounded model coefficients that maintains essential properties of the model coefficients, such as their weight in the model and the correlation matrix. In a certain sense, the risk score can be viewed as a transformation into a pre-selected scale. The risk score is generally represented as a point estimate. Thus, the risk-score index is a categorical variable that relates each and every category uniquely to risk. The main argument of this paper is that the risk score, which is calculated as a partial summation of rounded beta coefficients, is a statistic, and, therefore, it has its own variance. This variance is divided into three factors—the original β-coefficients variances, the rounding-error variance, and the variance from the relations between these two factors. Since the variance of the score is typically not negligible, it is preferable to consider the confidence interval centered at the point estimate and not just the point estimate itself. By using the confidence interval for the risk score, one can quantify the accuracy of the score and also compare different scores, which otherwise is not always possible.     

Gauge fixing,BRS invariance and Ward identities for randomly stirred flows

The Galilean invariance of the Navier–Stokes equation is shown to be akin to a global gauge symmetry familiar from quantum field theory. This symmetry leads to a multiple counting of infinitely many inertial reference frames in the path integral approach to randomly stirred fluids. This problem is solved by fixing the gauge, i.e., singling out one reference frame. The gauge fixed theory has an underlying Becchi–Rouet–Stora (BRS) symmetry which leads to the Ward identity relating the exact inverse response and vertex functions. This identification of Galilean invariance as a gauge symmetry is explored in detail, for different gauge choices and by performing a rigorous examination of a discretized version of the theory. The Navier–Stokes equation is also invariant under arbitrary rectilinear frame accelerations, known as extended Galilean invariance (EGI). We gauge fix this extended symmetry and derive the generalized Ward identity that follows from the BRS invariance of the gauge-fixed theory. This new Ward identity reduces to the standard one in the limit of zero acceleration. This gauge-fixing approach unambiguously shows that Galilean invariance and EGI constrain only the zero mode of the vertex but none of the higher wavenumber modes.