Narrow Results

It was long assumed that the pseudorandom distribution of prime numbers was free of biases. Specifically, while the prime number theorem gives an asymptotic measure of the probability of finding a prime number and Dirichlet’s theorem on arithmetic progressions tells us about the distribution of primes across residue classes, there was no reason to believe that consecutive primes might “know” anything about each other — that they might, for example, tend to avoid ending in the same digit. Here, we show that the Iterated Function System method (IFS) can be a surprisingly useful tool for revealing such unintuitive results and for more generally studying structure in number theory. Our experimental findings from a study in 2013 include fractal patterns that reveal “repulsive” phenomena among primes in a wide range of classes having specific congruence properties. Some of the phenomena shown in our computations and interpretation relate to more recent work by Lemke Oliver and Soundararajan on biases between consecutive primes. Here, we explore and extend those results by demonstrating how IFS points to the precise manner in which such biases behave from a dynamic standpoint. We also show that, surprisingly, composite numbers can exhibit a notably similar bias.

Artificial Intelligence (AI) algorithms showcase the potential to steer a paradigm shift in clinical medicine, especially medical imaging. Concerns associated with model generalizability and biases necessitate rigorous external validation of AI algorithms prior to their adoption into clinical workflows. To address the barriers associated with patient privacy, intellectual property, and diverse model requirements, we introduce ClinValAI, a framework for establishing robust cloud-based infrastructures to clinically validate AI algorithms in medical imaging. By featuring dedicated workflows for data ingestion, algorithm scoring, and output processing, we propose an easily customizable method to assess AI models and investigate biases. Our novel orchestration mechanism facilitates utilizing the complete potential of the cloud computing environment. ClinValAI’s input auditing and standardization mechanisms ensure that inputs consistent with model prerequisites are provided to the algorithm for a streamlined validation. The scoring workflow comprises multiple steps to facilitate consistent inferencing and systematic troubleshooting. The output processing workflow helps identify and analyze samples with missing results and aggregates final outputs for downstream analysis. We demonstrate the usability of our work by evaluating a state-of-the-art breast cancer risk prediction algorithm on a large and diverse dataset of 2D screening mammograms. We perform comprehensive statistical analysis to study model calibration and evaluate performance on important factors, including breast density, age, and race, to identify latent biases. ClinValAI provides a holistic framework to validate medical imaging models and has the potential to advance the development of generalizable AI models in clinical medicine and promote health equity.

We introduce an information theoretic framework for a quantitative measure of originality to model the impact of various classes of biases, errors and error corrections on scientific research. Some of the open problems are also outlined.

Innovations in human-centered biomedical informatics are often developed with the eventual goal of real-world translation. While biomedical research questions are usually answered in terms of how a method performs in a particular context, we argue that it is equally important to consider and formally evaluate the ethical implications of informatics solutions. Several new research paradigms have arisen as a result of the consideration of ethical issues, including but not limited for privacy-preserving computation and fair machine learning. In the spirit of the Pacific Symposium on Biocomputing, we discuss broad and fundamental principles of ethical biomedical informatics in terms of Olelo Noeau, or Hawaiian proverbs and poetical sayings that capture Hawaiian values. While we emphasize issues related to privacy and fairness in particular, there are a multitude of facets to ethical biomedical informatics that can benefit from a critical analysis grounded in ethics.

This paper examines the performance of a new probability model developed in terms of the surface area and velocity of an aero-structure, and presents some relevant statistical inferences. Several examples will compare the robustness of three kinds of point estimators developed for the lift coefficient. Four different types of confidence intervals for the lift coefficient are also developed, and it is shown that the shortest length confidence interval is an UMA confidence interval. Using the probability model, the correlation coefficient between lift and velocity, and the relevant regression slope are computed. The inferences and the results of this paper can be used particularly in the designing process of an aero-structure, especially when there is some uncertainty about its surface area; this provides some flexibilities for aerodynamicists in determining some of the unknown design characteristics.

Phase error of the demodulation clock in the Coriolis vibratory gyroscope system allows the quadrature errors to leak into the sense channel and causes significant bias and temperature drift at the rate output. A phase self-correction method to suppress the temperature drift of the bias in gyroscopes is proposed. Through sweeping the demodulation clock phase and simultaneously monitoring the mechanical quadrature error output in gyroscopes, the optimal demodulation clock phase with minimum relatively phase shift is determined. Thus the bias influenced by the temperature and surroundings can be calibrated on-chip at start-up or when the environment changes drastically without the requirement of the complicated instruments. The proposed approach is validated by a silicon MEMS gyroscope with the natural frequency of 2.8kHz, which shows nearly 22 times improvement in the temperature sensitivity of the system bias, from 550mdeg/s/^∘C down to 24.7mdeg/s/^∘C.

Rising acceptance of machine learning driven decision support systems underscores the need for ensuring fairness for all stakeholders. This work proposes a novel approach to increase a Neural Network model’s fairness during the training phase. We offer a frame-work to create a family of diverse fairness enhancing regularization components that can be used in tandem with the widely accepted binary-cross-entropy based accuracy loss. We use Bias Parity Score (BPS), a metric that quantifies model bias with a single value, to build loss functions pertaining to different statistical measures — even for those that may not be developed yet. We analyze behavior and impact of the newly minted regularization components on bias. We explore their impact in the realm of recidivism and census-based adult income prediction. The results illustrate that apt fairness loss functions can mitigate bias without forsaking accuracy even for imbalanced datasets.

Titanium (Ti) thin films with (002) or (100) texture are favored for many applications. In this paper, Ti thin films were prepared by high-power pulsed magnetron sputtering, and the texture of Ti thin films was successfully tailored by adjusting the pulse width, substrate bias and magnetic field strength. It is found that the peak power and average power of the Ti target are increased by increasing sputtering pulse width and decreasing magnetic field strength, which raise the Ti plasma flux and ion/atom ratio of Ti ions in front of the substrate simultaneously. Ti thin films with a highly (002) out-of-plane texture can be obtained with higher pulse width and lower magnetic field strength. The Ti thin films with highly (100) out-of-plane texture can be achieved with shorter pulse width, lower magnetic field strength and substrate bias.

Accurately identifying the various types of knee osteoarthritis aids in an accurate diagnosis. The unique kind and severity of osteoarthritis enable medical specialists to offer the best management and treatment plans. Knee osteoarthritis greatly affects the living style of people by causing higher anxiety, mental issues, and health issues. Early treatment is possible because of early prediction, which may improve patient outcomes. Individuals may be able to prevent or postpone the development of knee osteoarthritis symptoms. An efficient categorization method for knee osteoarthritis employing the Military Scrutolf optimization-tuned deep Convolutional Neural Network (MSO-DCNN) and the advancement of study into this crippling disorder and the improvement of diagnosis, therapy, resource allocation, and disease monitoring are all made possible by the CNN classifier. The preprocessing of the data, which is carried out in three parts and involves the Circular Fourier Transform, Histogram Equalization, and Multivariate Linear Function, also contributes significantly to the success of this study. The proposed MSO technique, which improves convergence time and fine-tunes the classifier’s weight and Bias parameters, was built utilizing the features of military dogs and scrutolf to assist in getting increased seeking and hunting qualities. The MSO-tuned DCNN classifier’s adjusted weights and bias to give more effective desired classification results without using up more time or storage. By examining the performance measures and comparing the existing techniques to the MDO-based DCNN, the suggested MSO-DCNN improved based on TP accuracy by 1.33%, f1 measure by 2.9%, precision by 0.8%, and recall by 2.905%.

One of the most important objectives of statistical inference is to estimate unknown model parameters based on an observed data. In this chapter, we will introduce some fundamental estimation methods for distributional model parameters. In particular, the maximum likelihood estimation and the method of moments estimation/generalized method of moments estimation are discussed, and their asymptotic properties investigated. Then we will discuss the methods for evaluating parameter estimators using the mean squared error criterion. The Lagrange multiplier method and the Cramer-Rao lower bound are used to derive the best unbiased estimators.

This paper presents a 65nm CMOS low-power, highly linear variable gain amplifier (VGA) suitable for biomedical applications. Typical biological signal amplitudes are in the 0.5–100mV range, and therefore require circuits with a wide dynamic range. Existing VGA architectures mostly exhibit a poor linearity, due to very low local feedback loop-gain. A technique to increase the loop-gain has been explored by adding additional feedback to the tail current source of the input differential pair. Stability analysis of the proposed technique was undertaken with pole-zero analysis. A prototype of Analog Front End (AFE) has been designed to provide 25–50 dB gain, and post-layout simulations showed a 15dB reduction in the harmonic distortion for 20mV pk-pk input signal compared to the conventional architecture. The circuit occupies 3,108$\mu$m² silicon area and consumes 0.43 $\mu$A from a 1.2V power supply.

This paper presents some novel entropy estimators of a continuous random variable using simple random sampling (SRS), ranked set sampling (RSS), and double RSS (DRSS) schemes. The theoretical results of the proposed entropy estimators are derived. The proposed entropy estimators are compared in terms of the bias and the root mean squared errors, theoretically and numerically, with the Vasicek O. [A test for normality based on sample entropy, J. R. Stat. Soc. B38:54–59, 1976.] entropy estimators using SRS, RSS, and DRSS schemes. It turns out that the new novel entropy estimators are substantially better than the existing Vasicek’s entropy estimators.

We present design considerations for high speed high swing differential modulator drivers in SiGeBiCMOS technology. Trade-offs between lumped and distributed designs, and linear and limiting amplifiers are examined. The design of a 6 V output modulator driver is discussed in detail. The driver features a unique bias generation and distribution circuit that enables low power-supply operation. Simulation results and measurements are given.

We report on a theoretical study of magnetoresistance (MR) effect in a magnetically modulated semiconductor heterostructure (MMSH) under an applied bias, which can be constructed on surface of ${\mathrm{\text{GaAs/Al}}}_x{\mathrm{\text{Ga}}}_{1-x}\mathrm{\text{As}}$ heterostructure by depositing two asymmetric ferromagnetic (FM) stripes. Bias-dependent transmission and conductance are calculated numerically, on the basis of both improved transfer matrix method (ITMM) and Landauer–Büttiker conductance theory. An obvious MR effect appears because of a significant difference of transmission between parallel and antiparallel (AP) magnetization configurations. Moreover, MR ratio can be tuned by the bias. These interesting features not only provide an alternative way to manipulate MR effect, but also may lead to an electrically-controllable MR device.

Using convexity properties of reciprocals of zeta functions, especially the reciprocal of the Riemann zeta function, we show that certain weighted Mertens sums are biased in favor of square-free integers with an odd number of prime factors. We study such type of bias for different ranges of the parameters and then consider generalizations to Mertens sums supported on semigroups of integers generated by relatively large subsets of prime numbers. We further obtain a wider range for the parameters both unconditionally and then conditionally on the Riemann Hypothesis. At the same time, we extend to certain semigroups, two classical summation formulas originating from the works of Landau concerning the behavior of derivatives of the reciprocal of the Riemann zeta function at $s=1$.

This study examines the accuracy and bias associated with the analysts' earnings forecasts of Taiwanese firms. Using the forecast data of individual analysts over 1991–1997 from the I/B/E/S database, we find that analysts' forecasts of earnings are generally more accurate than the predictions of a naïve forecasting model. However, this superiority seems to be largely confined to shorter forecast horizons. We also find that the analysts' earnings forecasts of Taiwanese firms are optimistically biased and that the bias depends on the nature of the earnings news. In addition, analysts' forecasts appear to be more accurate for larger firms and the bias also decreases with firm size. We find some variation in forecast accuracy and bias across industries but the overall results are not driven by any specific time period.

A single-mode buried heterostructure laser has been imaged using Cross-Sectional Scanning Tunneling Microscopy (X-STM). The problem of positioning the tip on the restricted active region on the (110) face has been overcome using combined Scanning Electron Microscopy (SEM).

In order to understand the change in the STM scans when biased, particularly the physical change in surface step defects caused by commercial sample preparation, the experimental setup has been modified to allow the sample to be biased. A simpler double quantum well test structure has been biased and it has been demonstrated that it is possible to continue performing STM whilst the device is powered. The change in the relative contrast across the image has been shown to be unaffected by this external bias for the range scanned, as predicted by a fully-coupled Poison drift–diffusion model calculated using Fermi–Dirac statistics.

This paper examines the performance of a new probability model developed in terms of the surface area and velocity of an aero-structure, and presents some relevant statistical inferences. Several examples will compare the robustness of three kinds of point estimators developed for the lift coefficient. Four different types of confidence intervals for the lift coefficient are also developed, and it is shown that the shortest length confidence interval is an UMA confidence interval. Using the probability model, the correlation coefficient between lift and velocity, and the relevant regression slope are computed. The inferences and the results of this paper can be used particularly in the designing process of an aero-structure, especially when there is some uncertainty about its surface area; this provides some flexibilities for aerodynamicists in determining some of the unknown design characteristics.

In this paper the familial risk factors related to type 1 diabetes is studied. The analysis is based on data collected during epidemiological research performed from 1989–1996 in Upper Silesia, Poland. Different statistical models that allow for evaluating risk factors are discussed and applied to the data.

The object of this research is to present a theoretical model about the process of management perception of the factors which intervene in the export decision (strategic interest and accessibility to overseas markets). With that aim, the phases which constitute the perception process are identified — the selection of stimuli and interpretation — and the associated bias. Specifically, we identify two: bias by omission and bias by imprecise meaning. The use of different sources of information as well as the influence of the network of relations of the management allows us to investigate thoroughly the filters through which the informative stimuli pass which converge in the decision to export.