Quadrupolar quantum criticality on a fractal

We study the ground state ordering of quadrupolar ordered $S=1$ magnets as a function of spin dilution probability $p$ on the triangular lattice. In sharp contrast to the ordering of $S=1/2$ dipolar N\'eel magnets on percolating clusters, we find that the quadrupolar magnets are quantum disordered at the percolation threshold, $p=p^*$. Further we find that long-range quadrupolar order is present for all $p<p^*$ and vanishes first exactly at $p^*$. Strong evidence for scaling behavior close to $p^*$ points to an unusual quantum criticality without fine tuning that arises from an interplay of quantum fluctuations and randomness

Initial Wage, Human Capital and Post Wage Differentials

Insufficiency in information with which firms judge the productivity of a worker for the first time in the market creates more randomness in initial wages than in later wages. This paper examines whether the initial randomness in wages may have a persistent effecton post wages. We set up a human capital accumulation in which an individual may respond to the positive error in initial wage by adjusting hours worked thereafter in her career, and consequently may receive higher future wages than those who draw a negative error in initial wages but otherwise are equivalent. The model predicts that the initial wage, in particular, its random component, is a persistently important factor having positive effecton future wages. Using data from the National Longitudinal Survey of Youth 79, we find empirical evidence that this effect is indeed positive and persists even after 20 years since the initial entry to labor market. The decomposition of initial wages by both parametric and nonparametric IV methods further shows that this effectis derived by the random component, nott he observable component, of the initial wage. It implies that the observed cross-sectional wage variation within group can be accounted for the initial randomness in wages.Human Capital Accumulation, Learning, Initial Wage, Wage Differentials

Investigating Chaos on the Johannesburg Stock Exchange

This study investigates the existence of chaos on the Johannesburg Stock Exchange (JSE) and studies three indices namely the FTSE/JSE All Share, FTSE/JSE Top 40 and FTSE/JSE Small Cap. Building upon the Fractal Market Hypothesis to provide evidence on the behavior of returns time series of the above mentioned indices, the BDS test is applied to test for non-random chaotic dynamics and further applies the rescaled range analysis to ascertain randomness, persistence or mean reversion on the JSE. The BDS test shows that all the indices examined in this study do not exhibit randomness. The FTSE/JSE All Share Index and the FTSE/JSE Top 40 exhibit slight reversion to the mean whereas the FTSE/JSE Small Cap exhibits significant persistence and appears to be less risky relative to the FTSE/JSE All Share and FTSE/JSE Top 40contrary to the assertion that small cap indices are riskier than large cap indices

Floating of Extended States and Localization Transition in a Weak Magnetic Field

We report results of a numerical study of non-interacting electrons moving in a random potential in two dimensions in the presence of a weak perpendicular magnetic field. We study the topological properties of the electronic eigenstates within a tight binding model. We find that in the weak magnetic field or strong randomness limit, extended states float up in energy. Further, the localization length is found to diverge at the insulator phase boundary with the same exponent $\nu$ as that of the isolated lowest Landau band (high magnetic field limit).Comment: RevTex, 4 pages, 3 figures available upon reques

Derandomized Novelty Detection with FDR Control via Conformal E-values

Conformal prediction and other randomized model-free inference techniques are gaining increasing attention as general solutions to rigorously calibrate the output of any machine learning algorithm for novelty detection. This paper contributes to the field by developing a novel method for mitigating their algorithmic randomness, leading to an even more interpretable and reliable framework for powerful novelty detection under false discovery rate control. The idea is to leverage suitable conformal e-values instead of p-values to quantify the significance of each finding, which allows the evidence gathered from multiple mutually dependent analyses of the same data to be seamlessly aggregated. Further, the proposed method can reduce randomness without much loss of power, partly thanks to an innovative way of weighting conformal e-values based on additional side information carefully extracted from the same data. Simulations with synthetic and real data confirm this solution can be effective at eliminating random noise in the inferences obtained with state-of-the-art alternative techniques, sometimes also leading to higher power.Comment: 19 pages, 11 figure

Skewness and Kurtosis in Statistical Kinetics

We obtain lower and upper bounds on the skewness and kurtosis associated with the cycle completion time of unicyclic enzymatic reaction schemes. Analogous to a well known lower bound on the randomness parameter, the lower bounds on skewness and kurtosis are related to the number of intermediate states in the underlying chemical reaction network. Our results demonstrate that evaluating these higher order moments with single molecule data can lead to information about the enzymatic scheme that is not contained in the randomness parameter.Comment: 5+3 pages, 4 figure

Algorithmic Randomness as Foundation of Inductive Reasoning and Artificial Intelligence

This article is a brief personal account of the past, present, and future of algorithmic randomness, emphasizing its role in inductive inference and artificial intelligence. It is written for a general audience interested in science and philosophy. Intuitively, randomness is a lack of order or predictability. If randomness is the opposite of determinism, then algorithmic randomness is the opposite of computability. Besides many other things, these concepts have been used to quantify Ockham's razor, solve the induction problem, and define intelligence.Comment: 9 LaTeX page