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In this paper, we will provide a result on the relativistic Euler equations for an ideal gas equation of state and a physical vacuum boundary. More specifically, we will prove a priori estimates for the linearized system in weighted Sobolev spaces. Our focus will be on choosing the correct thermodynamic variables, developing a weighted book-keeping scheme, and then proving energy estimates for the linearized system.

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 derive precise asymptotics for the time to converge to stationarity (mixing time) as the population size becomes large. It turns out that the chain exhibits the cutoff phenomenon, which is a sharp transition in time from one to zero of the total variation distance to stationarity. We obtain the exact leading constant for the cutoff time, and show the window size is constant (optimal) order. 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 for the trajectory of the chain, and coupling techniques., Comment: Ver2: 27 pages, additional details and discussion of related results; Ver1: 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. Second version addresses comments from referee reports

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