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Confidence estimates are often "detection-like" - driven by positive evidence in favour of a decision. This empirical observation has been interpreted as showing human metacognition is limited by biases or heuristics. Here we show that Bayesian confidence estimates also exhibit heightened sensitivity to decision-congruent evidence in higher-dimensional signal detection theoretic spaces, leading to detection-like confidence criteria. This effect is due to a nonlinearity induced by normalisation of confidence by a large number of unchosen alternatives. Our analysis suggests that detection-like confidence is rational when computing confidence in a higher-dimensional evidence space than that assumed by the experimenter.

We study a variant of the classical Markovian logistic SIS epidemic model on a complete graph, which has the additional feature that healthy individuals can become infected without contacting an infected member of the population. This additional ``self-infection'' is used to model situations where there is an unknown source of infection or an external disease reservoir, such as an animal carrier population. In contrast to the classical logistic SIS epidemic model, the version with self-infection has a non-degenerate stationary distribution, and we show that it exhibits the cutoff phenomenon, which is a sharp transition in time from one to zero of the total variation distance to stationarity. While this result is interesting in its own right, an additional contribution of our work is that the proof illustrates a recently formalised methodology of Barbour, Brightwell and Luczak, which can be used to show cutoff via a combination of concentration of measure inequalities and coupling techniques., Comment: 26 pages

Solving a long standing conjecture of Erd\H{o}s and Simonovits, Brandt and Thomass\'e proved that the chromatic number of each triangle-free graph $G$ such that $\delta(G)>|V(G)|/3$ is at most four. In fact, they showed the much stronger result that every maximal triangle-free graph $G$ satisfying this minimum degree condition is a blow-up of either an Andr\'asfai or a Vega graph. Here we establish the same structural conclusion on $G$ under the weaker assumption that for $m\in\{2, 3, 4\}$ every sequence of $3m$ vertices has a subsequence of length $m+1$ with a common neighbour. In forthcoming work this will be used to solve an old problem of Andr\'asfai in Ramsey-Tur\'an theory., Comment: 34 figures

The paper is devoted to the investigation of Segal's entropy in semifinite von Neumann algebras. The following questions are dealt with: semicontinuity, the 'ideal-like' structure of the linear span of the set of operators with finite entropy, and topological properties of the set of operators with finite as well as infinite entropy. In our analysis, full generality is aimed at, in particular, the operators for which the entropy is considered are not assumed to belong to the underlying von Neumann algebra, instead, they are arbitrary positive elements in the space $L^1$ over the algebra.

We show that there exists an absolute constant $A$ such that the size Ramsey number of a pair of cycles $(C_n$, $C_{2d})$, where $4\le 2d\le n$, is bounded from above by $An$. We also study the restricted size Ramsey number for such a pair., Comment: 14 pages

Let $\mathrm{ex}(n,s)$ denote the maximum number of edges in a triangle-free graph on $n$ vertices which contains no independent sets larger than $s$. The behaviour of $\mathrm{ex}(n,s)$ was first studied by Andr\'asfai, who conjectured that for $s>n/3$ this function is determined by appropriately chosen blow-ups of so called Andr\'asfai graphs. Moreover, he proved $\mathrm{ex}(n, s)=n^2-4ns+5s^2$ for $s/n\in [2/5, 1/2]$ and in earlier work we obtained $\mathrm{ex}(n, s)=3n^2-15ns+20s^2$ for $s/n\in [3/8, 2/5]$. Here we make the next step in the quest to settle Andr\'asfai's conjecture by proving $\mathrm{ex}(n, s)=6n^2-32ns+44s^2$ for $s/n\in [4/11, 3/8]$., Comment: Dedicated to the memory of Vera T. S\'os

In this work, we investigate the inference time of the MobileNet family, EfficientNet V1 and V2 family, VGG models, Resnet family, and InceptionV3 on four edge platforms. Specifically NVIDIA Jetson Nano, Intel Neural Stick, Google Coral USB Dongle, and Google Coral PCIe. Our main contribution is a thorough analysis of the aforementioned models in multiple settings, especially as a function of input size, the presence of the classification head, its size, and the scale of the model. Since throughout the industry, those architectures are mainly utilized as feature extractors we put our main focus on analyzing them as such. We show that Google platforms offer the fastest average inference time, especially for newer models like MobileNet or EfficientNet family, while Intel Neural Stick is the most universal accelerator allowing to run most architectures. These results should provide guidance for engineers in the early stages of AI edge systems development. All of them are accessible at https://bulletprove.com/research/edge_inference_results.csv

This article summarizes the literature on trust of digital technologies from a human-centric perspective. We summarize literature on trust in face-to-face interactions from other fields, followed by a discussion of organizational trust, technology-mediated trust, trust of software products, trust of AI, and blockchain. This report was created for the Science for Technological Innovation Veracity Spearhead supported by New Zealand's National Science Challenges.

The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discrete-time abstract parabolic systems are established by taking a nonparametric approach in the context of a mixed effects statistical model using a Prohorov metric framework on a set of feasible measures. A theoretical convergence result for a finite dimensional approximation scheme for computing the maximum likelihood estimator is also established and the efficacy of the approach is demonstrated by applying the scheme to the transdermal transport of alcohol modeled by a random parabolic PDE. Numerical studies included show that the maximum likelihood estimator is statistically consistent in that the convergence of the estimated distribution to the "true" distribution is observed in an example involving simulated data. The algorithm developed is then applied to two datasets collected using two different transdermal alcohol biosensors. Using the leave-one-out cross-validation method, we get an estimate for the distribution of the random parameters based on a training set. The input from a test drinking episode is then used to quantify the uncertainty propagated from the random parameters to the output of the model in the form of a 95% error band surrounding the estimated output signal., Comment: arXiv admin note: text overlap with arXiv:2304.11806

We consider a Prohorov metric-based nonparametric approach to estimating the probability distribution of a random parameter vector in discrete-time abstract parabolic systems. We establish the existence and consistency of a least squares estimator. We develop a finite-dimensional approximation and convergence theory, and obtain numerical results by applying the nonparametric estimation approach and the finite-dimensional approximation framework to a problem involving an alcohol biosensor, wherein we estimate the probability distribution of random parameters in a parabolic PDE. To show the convergence of the estimated distribution to the "true" distribution, we simulate data from the "true" distribution, apply our algorithm, and obtain the estimated cumulative distribution function. We then use the Markov Chain Monte Carlo Metropolis Algorithm to generate random samples from the estimated distribution, and perform a generalized (2-dimensional) two-sample Kolmogorov-Smirnov test with null hypothesis that our generated random samples from the estimated distribution and generated random samples from the "true" distribution are drawn from the same distribution. We then apply our algorithm to actual human subject data from the alcohol biosensor and observe the behavior of the normalized root-mean-square error (NRMSE) using leave-one-out cross-validation (LOOCV) under different model complexities.

There has been concern about ideological basis and possible discrimination in text generated by Large Language Models (LLMs). We test possible value biases in ChatGPT using a psychological value theory. We designed a simple experiment in which we used a number of different probes derived from the Schwartz basic value theory (items from the revised Portrait Value Questionnaire, the value type definitions, value names). We prompted ChatGPT via the OpenAI API repeatedly to generate text and then analyzed the generated corpus for value content with a theory-driven value dictionary using a bag of words approach. Overall, we found little evidence of explicit value bias. The results showed sufficient construct and discriminant validity for the generated text in line with the theoretical predictions of the psychological model, which suggests that the value content was carried through into the outputs with high fidelity. We saw some merging of socially oriented values, which may suggest that these values are less clearly differentiated at a linguistic level or alternatively, this mixing may reflect underlying universal human motivations. We outline some possible applications of our findings for both applications of ChatGPT for corporate usage and policy making as well as future research avenues. We also highlight possible implications of this relatively high-fidelity replication of motivational content using a linguistic model for the theorizing about human values., Comment: 26 pages, 4 Figures, 5 Tables

We investigate the situation when a normal positive linear unital map on a semifinite von Neumann algebra leaving the trace invariant does not change fixed quantum Renyi's entropy of the density of a normal state. It is also shown that such a map does not change the entropy of any density if and only if it is a Jordan *-isomorphism on the algebra.

The LOPES experiment was a radio interferometer built at the existing air shower array KASCADE-Grande in Karlsruhe, Germany. The last configuration of LOPES was called LOPES 3D and consisted of ten tripole antennas. Each of these antennas consisted of three crossed dipoles east-west, north-south, and vertically aligned. With this, LOPES 3D had the unique possibility to study the benefits of measurements with vertically aligned antennas in the environment of the well understood and calibrated particle detector array KASCADE-Grande. The measurements with three spatially coincident antennas allows a redundant reconstruction of the electric field vector. Several methods to exploit the redundancy were developed and tested. Furthermore, for the first time in LOPES, the background noise could be studied polarization- and direction dependent. With LOPES 3D it could be demonstrated that radio detection reaches a higher efficiency for inclined showers when including measurements with vertically aligned antennas and that the vertical component gets more important for the measurement of inclined showers. In this contribution we discuss a weighting scheme for the best combination of three redundant reconstructed electric field vectors. Furthermore, we discuss the influence of these weighting schemes on the ability to reconstruct air showers using the radio method. We show an estimate of the radio efficiency for inclined showers with focus on the benefits of measurements with vertically aligned antennas and we present the direction dependent noise in the different polarizations., Comment: Submission to the proceedings of the ARENA2014 workshop, which unfortunately were never published; thus documented here for reference

For graphs $H_1,H_2$ by $r^*(H_1,H_2)$ we denote the minimum number of edges in a graph $G$ on $r(H_1,H_2)$ vertices such that $G\to (H_1,H_2)$. We show that for each pair of natural numbers $k,n$, $k\le n$, where $k$ is odd and $n$ is large enough, we have $$r^*(C_n,C_k)=\lceil (n+1)(2n-1)/2\rceil \,.$$

Random walks can reveal communities or clusters in networks, because they are more likely to stay within a cluster than leave it. Thus, one family of community detection algorithms uses random walks to measure distance between pairs of nodes in various ways, and then applies K-Means or other generic clustering methods to these distances. Interestingly, information processing in the brain may suggest a simpler method of learning clusters directly from random walks. Drawing inspiration from the hippocampus, we describe a simple two-layer neural learning framework. Neurons in one layer are associated with graph nodes and simulate random walks. These simulations cause neurons in the second layer to become tuned to graph clusters through simple associative learning. We show that if these neuronal interactions are modelled a particular way, the system is essentially a variant of K-Means clustering applied directly in the walk-space, bypassing the usual step of computing node distances/similarities. The result is an efficient graph clustering method. Biological information processing systems are known for high efficiency and adaptability. In tests on benchmark graphs, our framework demonstrates this high data-efficiency, low memory use, low complexity, and real-time adaptation to graph changes, while still achieving clustering quality comparable to other algorithms., Comment: 10 pages, 8 figures

Developments in reinforcement learning (RL) have allowed algorithms to achieve impressive performance in highly complex, but largely static problems. In contrast, biological learning seems to value efficiency of adaptation to a constantly-changing world. Here we build on a recently-proposed neuronal learning rule that assumes each neuron can optimize its energy balance by predicting its own future activity. That assumption leads to a neuronal learning rule that uses presynaptic input to modulate prediction error. We argue that an analogous RL rule would use action probability to modulate reward prediction error. This modulation makes the agent more sensitive to negative experiences, and more careful in forming preferences. We embed the proposed rule in both tabular and deep-Q-network RL algorithms, and find that it outperforms conventional algorithms in simple, but highly-dynamic tasks. We suggest that the new rule encapsulates a core principle of biological intelligence; an important component for allowing algorithms to adapt to change in a human-like way., Comment: 9 pages, 5 figures

Since humans still outperform artificial neural networks on many tasks, drawing inspiration from the brain may help to improve current machine learning algorithms. Contrastive Hebbian Learning (CHL) and Equilibrium Propagation (EP) are biologically plausible algorithms that update weights using only local information (without explicitly calculating gradients) and still achieve performance comparable to conventional backpropagation. In this study, we augmented CHL and EP with Adjusted Adaptation, inspired by the adaptation effect observed in neurons, in which a neuron's response to a given stimulus is adjusted after a short time. We add this adaptation feature to multilayer perceptrons and convolutional neural networks trained on MNIST and CIFAR-10. Surprisingly, adaptation improved the performance of these networks. We discuss the biological inspiration for this idea and investigate why Neuronal Adaptation could be an important brain mechanism to improve the stability and accuracy of learning., Comment: 17 pages

We show that there are harmonic functions on a ball ${\mathbb{B}_n}$ of $\mathbb{R}^n$, $n\ge 2$, that are continuous up to the boundary (and even H\"older continuous) but not in the Sobolev space $H^s(\mathbb{B}_n)$ for any $s$ sufficiently big. The idea for the construction of these functions is inspired by the two-dimensional example of a harmonic continuous function with infinite energy presented by Hadamard in 1906. To obtain examples in any dimension $n\ge 2$ we exploit certain series of spherical harmonics. As an application, we verify that the regularity of the solutions that was proven for a class of boundary value problems with nonlinear transmission conditions is, in a sense, optimal., Comment: 19 pages

KASCADE-Grande and its original array of KASCADE were dedicated to measure individual air showers of cosmic rays with great detail in the primary energy range of 100 TeV up to 1 EeV. The experiment has significantly contributed to investigations of the energy spectrum and chemical composition of cosmic rays in the transition region from galactic to extragalactic origin of cosmic rays as well as to the further development of hadronic interaction models through validity tests using the multi-detector information from KASCADE-Grande. Though the data accumulation was completed in 2013, the data analysis is still continuing. Recently, we investigate the reliability of the new hadronic interactions model of the Sibyll version 2.3d with the combined data from KASCADE and KASCADE-Grande, and compare it to the predictions of different hadronic interaction models. In addition, we update the web-based platform of the KASCADE Cosmic Ray Data Centre (KCDC), where now full datasets from KASCADE and KASCADE-Grande and the corresponding Monte-Carlo simulated events are available., Comment: Presented at the 37th International Cosmic Ray Conference (ICRC 2021)

This paper provides an additional probabilistic interpretation of the limiting functions for the SIR epidemic on the configuration model derived in the paper by Janson, Luczak and Windridge (2014)., Comment: 10 pages. arXiv admin note: substantial text overlap with arXiv:1308.5493

LOPES, the LOFAR prototype station, was an antenna array for cosmic-ray air showers operating from 2003 - 2013 within the KASCADE-Grande experiment. Meanwhile, the analysis is finished and the data of air-shower events measured by LOPES are available with open access in the KASCADE Cosmic Ray Data Center (KCDC). This article intends to provide a summary of the achievements, results, and lessons learned from LOPES. By digital, interferometric beamforming the detection of air showers became possible in the radio-loud environment of the Karlsruhe Institute of Technology (KIT). As a prototype experiment, LOPES tested several antenna types, array configurations and calibration techniques, and pioneered analysis methods for the reconstruction of the most important shower parameters, i.e., the arrival direction, the energy, and mass-dependent observables such as the position of the shower maximum. In addition to a review and update of previously published results, we also present new results based on end-to-end simulations including all known instrumental properties. For this, we applied the detector response to radio signals simulated with the CoREAS extension of CORSIKA, and analyzed them in the same way as measured data. Thus, we were able to study the detector performance more accurately than before, including some previously inaccessible features such as the impact of noise on the interferometric cross-correlation beam. These results led to several improvements, which are documented in this paper and can provide useful input for the design of future cosmic-ray experiments based on the digital radio-detection technique., Comment: Accepted for publication by EPJ C

We find the exact value of the Ramsey number $R(C_{2\ell},K_{1,n})$, when $\ell$ and $n=O(\ell^{10/9})$ are large. Our result is closely related to the behaviour of Tur\'an number $ex(N, C_{2\ell})$ for an even cycle whose length grows quickly with $N$.

We develop $M$-estimation and deconvolution methodology with the goal of making well-founded statistical inference on an individual's blood alcohol level based on noisy measurements of their skin alcohol content. We first apply our results to a nonlinear least squares estimator of the key parameter that specifies the blood/skin alcohol relation in a diffusion model, and establish its existence, consistency, and asymptotic normality. To make inference on the unknown underlying blood alchohol curve, we develop a basis space deconvolution approach with regulazation, and determine the asymptotic distribution of the error process, thus allowing us to compute uniform confidence bands on the curve. Simulation studies show agreement between the performance of our curve estimators and their asymptotic distributions at low noise levels, and we apply our methods to a real skin alcohol data set collected via a transdermal biosensor., Comment: 46 pages, 13 figures. This version adds a deconvolution method using a basis space approach with regularization in order to make inference on the true underlying blood alcohol curve, a subsequent derivation of the asymptotic error process and evaluations of the resulting theoretical uniform confidence bands via simulations

Given positive integers $n\ge s$, we let ${\mathrm{ex}}(n,s)$ denote the maximum number of edges in a triangle-free graph $G$ on $n$ vertices with $\alpha(G)\le s$. In the early sixties Andr\'{a}sfai conjectured that for $n/3

One of the oldest results in modern graph theory, due to Mantel, asserts that every triangle-free graphs on $n$ vertices has at most $\lfloor n^2/4\rfloor$ edges. About half a century later Andr\'asfai studied dense triangle-free graphs and proved that the largest triangle-free graphs on $n$ vertices without independent sets of size $\alpha n$, where $2/5\le \alpha < 1/2$, are blow-ups of the pentagon. More than 50 further years have elapsed since Andr\'asfai's work. In this article we make the next step towards understanding the structure of dense triangle-free graphs without large independent sets. Notably, we determine the maximum size of triangle-free graphs~$G$ on $n$ vertices with $\alpha (G)\ge 3n/8$ and state a conjecture on the structure of the densest triangle-free graphs $G$ with $\alpha(G) > n/3$. We remark that the case $\alpha(G) \le n/3$ behaves differently, but due to the work of Brandt this situation is fairly well understood., Comment: Revised according to referee reports

We show that for every $\eta>0$, there exists $n_0$ such that for every even $n$, $n\ge n_0$, and every graph $G$ with $(2+\eta)n$ vertices and minimum degree at least $(7/4+4\eta)n$, each colouring of the edges of $G$ with three colours results in a monochromatic cycle of length $n$.