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We present some results concerning the relative modular operator in semifinite von Neumann algebras. These results allow one to prove some basic formula for trace, to obtain equivalence between Araki's relative entropy and Umegaki's information as well as to derive some formulae for quasi-entropies, and R\'enyi's relative entropy known in finite dimension.

Over the past 20 years, KASCADE and its extension KASCADE-Grande were dedicated to measure high-energy cosmic rays with primary energies of 100 TeV to 1 EeV. The data accumulation was fully completed and all experimental components were dismantled, though the analysis of the high-quality data is still continued. E.g., we investigated the validity of the hadronic interaction model of the new SIBYLL version 2.3c. We also published a new result of a search for large-scale anisotropies performed with the KASCADE-Grande data. Investigation of the attenuation length of the muon in the atmosphere is also updated with the predictions of the SIBYLL 2.3 interaction model. We investigated, in addition, the muon content of high-energy air showers and compared them to all post-LHC interaction models. In this contribution, the new and updated results from KASCADE-Grande will be presented. An update of the web-based data center KCDC offering the original scientific data from KASCADE-Grande to the public will be briefly discussed as well., Comment: Proceedings of the 36th ICRC 2019, Madison, USA

In this paper I conceptualise a novel approach for capturing coincidences between events that have not necessarily an observed causal relationship. Building on the Transcendental Information Cascades approach I outline a tensor theory of the interaction between rare micro-level events and macro-level system changes. Afterwards, I discuss a number of application areas that are promising candidates for the validation of the theoretical assumptions outlined here in practice. This is preliminary work that is sought to lay the foundation to discover universal mathematical properties of coincidences that have a measurable impact on the macroscopic state of a complex system and are therefore to be considered meaningful., Comment: 13 pages, this conceptual paper is based on a number of talks I gave on the underlying idea and synthesises a research programme that is work in progress

Measuring international research collaboration is necessary when evaluating, for example, the efficacy of policy meant to increase cooperation between countries, but is currently very difficult as bibliographic records contain only affiliation data from which there is no standard method to identify the relevant countries. In this paper we describe a method to address this difficulty, and evaluate it using both general and domain-specific data sets., Comment: This paper was accepted for publication at the 17th INTERNATIONAL CONFERENCE ON SCIENTOMETRICS & INFORMETRICS (ISSI 2019)

International research collaboration (IRC) measurement is important because countries can and want to benefit from international collaboration but performing the same measurement procedure on different data sets can lead to different results. This study aims to explore the effects of data set choice on IRC measurement., Comment: This paper was accepted for publication at the 17th INTERNATIONAL CONFERENCE ON SCIENTOMETRICS & INFORMETRICS (ISSI 2019)

We present studies of the electron transport and circular currents induced by the bias voltage and the magnetic flux threading a ring of three quantum dots coupled with two electrodes. Quantum interference of electron waves passing through the states with opposite chirality plays a relevant role in transport, where one can observe Fano resonance with destructive interference. The quantum interference effect is quantitatively described by local bond currents and their correlation functions. Fluctuations of the transport current are characterized by the Lesovik formula for the shot noise, which is a composition of the bond current correlation functions. In the presence of circular currents, the cross-correlation of the bond currents can be very large, but it is negative and compensates for the large positive auto-correlation functions., Comment: 10 pages, 8 figures, minor improvments

The influence of Web search personalisation on professional knowledge work is an understudied area. Here we investigate how public sector officials self-assess their dependency on the Google Web search engine, whether they are aware of the potential impact of algorithmic biases on their ability to retrieve all relevant information, and how much relevant information may actually be missed due to Web search personalisation. We find that the majority of participants in our experimental study are neither aware that there is a potential problem nor do they have a strategy to mitigate the risk of missing relevant information when performing online searches. Most significantly, we provide empirical evidence that up to 20% of relevant information may be missed due to Web search personalisation. This work has significant implications for Web research by public sector professionals, who should be provided with training about the potential algorithmic biases that may affect their judgments and decision making, as well as clear guidelines how to minimise the risk of missing relevant information., Comment: paper submitted to the 11th Intl. Conf. on Social Informatics; revision corrects error in interpretation of parameter Psi/p in RBO resulting from discrepancy between the documentation of the implementation in R (https://rdrr.io/bioc/gespeR/man/rbo.html) and the original definition (https://dl.acm.org/citation.cfm?id=1852106) as per 20/05/2019

We present new concentration of measure inequalities for Markov chains, generalising results for chains that are contracting in Wasserstein distance. These are particularly suited to establishing the cut-off phenomenon for suitable chains. We apply our discrete-time inequality to the well-studied Bernoulli-Laplace model of diffusion, and give a probabilistic proof of cut-off, recovering and improving the bounds of Diaconis and Shahshahani. We also extend the notion of cut-off to chains with an infinite state space, and illustrate this in a second example, of a two-host model of disease in continuous time. We give a third example, giving concentration results for the supermarket model, illustrating the full generality and power of our results., Comment: 60 pages; substantially revised in response to referee comments; accepted for publication in Stochastic Processes and Applications

We estimate the distribution of random parameters in a distributed parameter model with unbounded input and output for the transdermal transport of ethanol in humans. The model takes the form of a diffusion equation with the input being the blood alcohol concentration and the output being the transdermal alcohol concentration. Our approach is based on the idea of reformulating the underlying dynamical system in such a way that the random parameters are now treated as additional space variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating the diffusivity in a multi-dimensional diffusion equation and thus well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods may all be employed. We use our technique to estimate a bivariate normal distribution based on data for multiple drinking episodes from a single subject., Comment: 10 pages

A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed.

The distribution of random parameters in, and the input signal to, a distributed parameter model with unbounded input and output operators for the transdermal transport of ethanol are estimated. The model takes the form of a diffusion equation with the input, which is on the boundary of the domain, being the blood or breath alcohol concentration (BAC/BrAC), and the output, also on the boundary, being the transdermal alcohol concentration (TAC). Our approach is based on the reformulation of the underlying dynamical system in such a way that the random parameters are treated as additional spatial variables. When the distribution to be estimated is assumed to be defined in terms of a joint density, estimating the distribution is equivalent to estimating a functional diffusivity in a multi-dimensional diffusion equation. The resulting system is referred to as a population model, and well-established finite dimensional approximation schemes, functional analytic based convergence arguments, optimization techniques, and computational methods can be used to fit it to population data and to analyze the resulting fit. Once the forward population model has been identified or trained based on a sample from the population, the resulting distribution can then be used to deconvolve the BAC/BrAC input signal from the biosensor observed TAC output signal formulated as either a quadratic programming or linear quadratic tracking problem. In addition, our approach allows for the direct computation of corresponding credible bands without simulation. We use our technique to estimate bivariate normal distributions and deconvolve BAC/BrAC from TAC based on data from a population that consists of multiple drinking episodes from a single subject and a population consisting of single drinking episodes from multiple subjects.

The `KASCADE Cosmic ray Data Centre' is a web portal (\url{https://kcdc.ikp.kit.edu}), where the data of the astroparticle physics experiment KASCADE-Grande are made available for the interested public. The KASCADE experiment was a large-area detector for the measurement of high-energy cosmic rays via the detection of extensive air showers. The multi-detector installations KASCADE and its extension KASCADE-Grande stopped the active data acquisition in 2013 of all its components end of 2012 after more than 20 years of data taking. In several updates since our first release in 2013 with KCDC we provide the public measured and reconstructed parameters of more than 433 million air showers. In addition, KCDC provides meta data information and documentation to enable a user outside the community of experts to perform their own data analysis. Simulation data from three different high energy interaction models have been made available as well as a compilation of measured and published spectra from various experiments. In addition, detailed educational examples shall encourage high-school students and early stage researchers to learn about astroparticle physics, cosmic radiation as well as the handling of Big Data and about the sustainable and public provision of scientific data., Comment: 16 pages, submitted to The European Physical Journal C

In this paper we seek to contribute to the debate about the nature of citizen involvement in real scientific projects by the means of online tools that facilitate crowdsourcing and collaboration. We focus on an understudied area, the impact of online citizen science participation on the science education of school age children. We present a binary tree of online citizen science process flows and the results of an anonymous survey among primary school teachers in New Zealand that are known advocates of science education. Our findings reveal why teachers are interested in using online citizen science in classroom activities and what they are looking for when making their choice for a particular project to use. From these characteristics we derive recommendations for the optimal embedding of online citizen science in education related to the process, the context, and the dissemination of results., Comment: 16 pages, submitted to the 21st ACM Conference on Computer-Supported Cooperative Work and Social Computing (CSCW 2018)

We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic logistic SIS epidemic process, and we assume that there is perfect cross-immunity between the two strains, that is, individuals infected by one are temporarily immune to re-infections and infections by the other. For the case where one strain has a strictly larger basic reproductive ratio than the other, and the stronger strain on its own is supercritical (that is, its basic reproductive ratio is larger than 1), we derive precise asymptotic results for the distribution of the time when the weaker strain disappears from the population, that is, its extinction time. We further extend our results to certain parameter values where the difference between the two reproductive ratios may tend to 0 as $N \to \infty$. In proving our results, we illustrate a new approach to a fluid limit approximation for a sequence of Markov chains in the vicinity of a stable fixed point of the limit., Comment: 53 pages

The evolution of the muon content of very high energy air showers (EAS) in the atmosphere is investigated with data of the KASCADE-Grande observatory. For this purpose, the muon attenuation length in the atmosphere is obtained to $\Lambda_\mu = 1256 \, \pm 85 \, ^{+229}_{-232}(\mbox{syst})\, \mbox{g/cm}^2$ from the experimental data for shower energies between $10^{16.3}$ and $10^{17.0} \, \mbox{eV}$. Comparison of this quantity with predictions of the high-energy hadronic interaction models QGSJET-II-02, SIBYLL 2.1, QGSJET-II-04 and EPOS-LHC reveals that the attenuation of the muon content of measured EAS in the atmosphere is lower than predicted. Deviations are, however, less significant with the post-LHC models. The presence of such deviations seems to be related to a difference between the simulated and the measured zenith angle evolutions of the lateral muon density distributions of EAS, which also causes a discrepancy between the measured absorption lengths of the density of shower muons and the predicted ones at large distances from the EAS core. The studied deficiencies show that all four considered hadronic interaction models fail to describe consistently the zenith angle evolution of the muon content of EAS in the aforesaid energy regime., Comment: Published in Astroparticle Physics 95 (2017) 25-43

We consider a model of two interacting always-on, exchange-only qubits for which controlled phase ($CPHASE$), controlled NOT ($CNOT$), quantum Fourier transform ($QFT$) and $SWAP$ operations can be implemented only in a few electrical pulses in a nanosecond time scale. Each qubit is built of three quantum dots (TQD) in a triangular geometry with three electron spins which are always kept coupled by exchange interactions only. The qubit states are encoded in a doublet subspace and are fully electrically controlled by a voltage applied to gate electrodes. The two qubit quantum gates are realized by short electrical pulses which change the triangular symmetry of TQD and switch on exchange interaction between the qubits. We found an optimal configuration to implement the $CPHASE$ gate by a single pulse of the order 2.3 ns. Using this gate, in combination with single qubit operations, we searched for optimal conditions to perform the other gates: $CNOT$, $QFT$ and $SWAP$. Our studies take into account environment effects and leakage processes as well. The results suggest that the system can be implemented for fault tolerant quantum computations., Comment: 19 pages, 5 figures

Cosmic rays provide an unique approach to study hadronic interactions at high energies in the kinematic forward direction. The KASCADE air shower experiment was the first to conduct quantitative tests of hadronic interactions with air shower data. A brief overview is given on results from KASCADE and its extension KASCADE-Grande with respect to investigations of hadronic interactions and the properties of cosmic rays., Comment: presented at EDS Blois 2017, Prague, Czech Republic, June 26-30, 2017

KASCADE and KASCADE-Grande were multi-detector installations to measure individual air showers of cosmic rays at ultra-high energy. Based on data sets measured by KASCADE and KASCADE-Grande, 90% C.L. upper limits to the flux of gamma-rays in the primary cosmic ray flux are determined in an energy range of ${10}^{14} - {10}^{18}$ eV. The analysis is performed by selecting air showers with a low muon content as expected for gamma-ray-induced showers compared to air showers induced by energetic nuclei. The best upper limit of the fraction of gamma-rays to the total cosmic ray flux is obtained at $3.7 \times {10}^{15}$ eV with $1.1 \times {10}^{-5}$. Translated to an absolute gamma-ray flux this sets constraints on some fundamental astrophysical models, such as the distance of sources for at least one of the IceCube neutrino excess models., Comment: Published in The Astrophysical Journal, Volume 848, Number 1. Posted on: October 5, 2017

We discuss the chiral decomposition of non-symmetric stacking structures. It is shown that the low-energy electronic structure of Bernal stacked graphene multilayer deposited on h-BN consists of chiral pseudospin doublets. N-layer graphene stocks on h-BN layer have N/2 effective bilayer graphene systems and one effective h-BN layer if N is even or (N-1)/2 effective graphene bilayers plus one graphene monolayer modified by h-BN layer if N is odd. We present the decomposition procedure and we derive the recurrence relations for the effective parameters characterizing the chiral subsystems. The effective parameters consist in this case of the interlayer couplings and on-site potentials in contrast to pure graphene multilayer systems where only interlayer couplings are modified. We apply this procedure to discuss the Klein tunneling phenomena and compare quantitatively the results with pure graphene multilayer systems.

We show that for an infinitely many natural numbers $k$ there are $k$-uniform hypergraphs which admit a `rescaling phenomenon' as described in [9]. More precisely, let $\mathcal{A}(k,I, n)$ denote the class of $k$-graphs on $n$ vertices in which the sizes of all pairwise intersections of edges belong to a set $I$. We show that if $k=rt^2$ for some $r\ge 1$ and $t\ge 2$, and~$I$ is chosen in some special way, the densest graphs in $\mathcal{A}(rt^2,I, n)$ are either dominated by stars of large degree, or basically, they are `$t$-thick' $rt^2$-graphs in which vertices are partitioned into groups of $t$ vertices each and every edge is a union of $tr$ such groups. It is easy to see that, unlike in stars, the maximum degree of $t$-thick graphs is of a lower order than the number of its edges. Thus, if we study the graphs from $\mathcal{A}(rt^2,I, n)$ with a prescribed number of edges $m$ which minimize the maximum degree, around the value of $m$ which is the number of edges of the largest $t$-thick graph, a rapid, discontinuous phase transition can be observed. Interestingly, these two types of $k$-graphs determine the structure of all hypergraphs in $\mathcal{A}(rt^2,I, n)$. Namely, we show that each such hypergraph can be decomposed into a $t$-thick graph $H_T$, a special collection $H_S$ of stars, and a sparse `left-over' graph $H_R$., Comment: second version addresses changes arising from the referee reports

We study the Ramsey number for the 3-path of length three and $n$ colors and show that $R(P^3_3;n)\le \lambda_0 n+7\sqrt{n}$, for some explicit constant $\lambda_0=1.97466\dots$.

Let $P^k_\ell$ denote the loose $k$-path of length $\ell$ and let define $f^k_\ell(n,m)$ as the minimum value of $\Delta(H)$ over all $P^k_\ell$-free $k$-graphs $H$ with $n$ vertices and $m$ edges. In the paper we study the behavior of $f^4_2(n,m)$ and $f^3_3(n,m)$ and characterize the structure of extremal hypergraphs. In particular, it is shown that when $m\sim n^2/8$ the value of each of these functions drops down from $\Theta(n^2)$ to $\Theta(n)$.

We show that there exists an absolute constant $A$ such that for each $k\ge2$ and every coloring of the edges of the complete $k$-uniform hypergraph on $ Ar$ vertices with $r$ colors, one of the color classes contains a loose path of length three.

Location-based augmented reality games have entered the mainstream with the nearly overnight success of Niantic's Pok\'emon Go. Unlike traditional video games, the fact that players of such games carry out actions in the external, physical world to accomplish in-game objectives means that the large-scale adoption of such games motivate people, en masse, to do things and go places they would not have otherwise done in unprecedented ways. The social implications of such mass-mobilisation of individual players are, in general, difficult to anticipate or characterise, even for the short-term. In this work, we focus on disaster relief, and the short- and long-term implications that a proliferation of AR games like Pok\'emon Go, may have in disaster-prone regions of the world. We take a distributed cognition approach and focus on one natural disaster-prone region of New Zealand, the city of Wellington.

This paper presents the development of several models of a deep convolutional auto-encoder in the Caffe deep learning framework and their experimental evaluation on the example of MNIST dataset. We have created five models of a convolutional auto-encoder which differ architecturally by the presence or absence of pooling and unpooling layers in the auto-encoder's encoder and decoder parts. Our results show that the developed models provide very good results in dimensionality reduction and unsupervised clustering tasks, and small classification errors when we used the learned internal code as an input of a supervised linear classifier and multi-layer perceptron. The best results were provided by a model where the encoder part contains convolutional and pooling layers, followed by an analogous decoder part with deconvolution and unpooling layers without the use of switch variables in the decoder part. The paper also discusses practical details of the creation of a deep convolutional auto-encoder in the very popular Caffe deep learning framework. We believe that our approach and results presented in this paper could help other researchers to build efficient deep neural network architectures in the future., Comment: 21 pages, 11 figures, 5 tables, 62 references

The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in ${\mathbb Z}^d$. We illustrate the use of the method for sums of independent integer valued random vectors, and for random vectors exhibiting an exchangeable pair. We conclude with an application to random colourings of regular graphs., Comment: arXiv:1512.07400 has been split into two parts: this is Part II

We show that if we color the hyperedges of the complete $3$-uniform complete graph on $2n+\sqrt{18n+1}+2$ vertices with $n$ colors, then one of the color classes contains a loose path of length three.

We study near-critical behavior in the configuration model. Let $D_n$ be the degree of a random vertex. We let $\nu_n={\mathbb E} [D_n(D_n-1)]/{\mathbb E}[D_n]$ and, assuming that $\nu_n \to 1$ as $n \to \infty$, we write $\varepsilon_n=\nu_n-1$. We call the setting where $\varepsilon_n n^{1/3}/({\mathbb E}[D_n^3])^{2/3} \to \infty$ the {\it barely supercritical} regime. We further assume that the variance of $D_n$ is uniformly bounded as $n \to \infty$. Let $D_n^*$ denote the size-biased version of $D_n$. We prove that there is a unique giant component of size $n \rho_n {\mathbb E} D_n (1+o(1))$, where $\rho_n$ denotes the survival probability of a branching process with offspring distribution $D_n^*-1$. This extends earlier results of Janson and Luczak~\cite{JanLuc07}, as well as those of Janson, Luczak, Windridge and House~\cite{SJ300} to the case where the third moment of $D_n$ is unbounded, filling the gap in the literature. We further study the size of the largest component in the \emph{critical} regime, where $\varepsilon_n = O(n^{-1/3} ({\mathbb E} D_n^3)^{2/3})$, extending and complementing results of Hatami and Molloy~\cite{HatamiMolloy}., Comment: 46 pages

We study generation and dynamics of an exchange spin qubit encoded in three coherently coupled quantum dots with three electrons. For two geometries of the system a linear and a triangular one, the creation and coherent control of the qubit states are performed by the Landau--Zener transitions. In the triangular case both the qubit states are equivalent and can be easily generated for particular symmetries of the system. If one of the dots is smaller than the others one can observe Rabi oscillations, that can be used for coherent manipulation of the qubit states. The linear system is easier to fabricate; however, then the qubit states are not equivalent, making qubit operations more difficult to control., Comment: 17 pages, 5 figures

The radio technique is a promising method for detection of cosmic-ray air showers of energies around $100\,$PeV and higher with an array of radio antennas. Since the amplitude of the radio signal can be measured absolutely and increases with the shower energy, radio measurements can be used to determine the air-shower energy on an absolute scale. We show that calibrated measurements of radio detectors operated in coincidence with host experiments measuring air showers based on other techniques can be used for comparing the energy scales of these host experiments. Using two approaches, first via direct amplitude measurements, and second via comparison of measurements with air shower simulations, we compare the energy scales of the air-shower experiments Tunka-133 and KASCADE-Grande, using their radio extensions, Tunka-Rex and LOPES, respectively. Due to the consistent amplitude calibration for Tunka-Rex and LOPES achieved by using the same reference source, this comparison reaches an accuracy of approximately $10\,\%$ - limited by some shortcomings of LOPES, which was a prototype experiment for the digital radio technique for air showers. In particular we show that the energy scales of cosmic-ray measurements by the independently calibrated experiments KASCADE-Grande and Tunka-133 are consistent with each other on this level.

The random $2$-dimensional simplicial complex process starts with a complete graph on $n$ vertices, and in every step a new $2$-dimensional face, chosen uniformly at random, is added. We prove that with probability tending to $1$ as $n\to\infty$, the first homology group over $\mathbb Z$ vanishes at the very moment when all the edges are covered by triangular faces.

Graph symmetries intervene in diverse applications, from enumeration, to graph structure compression, to the discovery of graph dynamics (e.g., node arrival order inference). Whereas Erd\H{o}s-R\'enyi graphs are typically asymmetric, real networks are highly symmetric. So a natural question is whether preferential attachment graphs, where in each step a new node with $m$ edges is added, exhibit any symmetry. In recent work it was proved that preferential attachment graphs are symmetric for $m=1$, and there is some non-negligible probability of symmetry for $m=2$. It was conjectured that these graphs are asymmetric when $m \geq 3$. We settle this conjecture in the affirmative, then use it to estimate the structural entropy of the model. To do this, we also give bounds on the number of ways that the given graph structure could have arisen by preferential attachment. These results have further implications for information theoretic problems of interest on preferential attachment graphs., Comment: 24 pages; to appear in Random Structures & Algorithms

A sequence $S$ is called anagram-free if it contains no consecutive symbols $r_1 r_2\dots r_k r_{k+1} \dots r_{2k}$ such that $r_{k+1} \dots r_{2k}$ is a permutation of the block $r_1 r_2\dots r_k$. Answering a question of Erd\H{o}s and Brown, Ker\"anen constructed an infinite anagram-free sequence on four symbols. Motivated by the work of Alon, Grytczuk, Ha\l uszczak and Riordan, we consider a natural generalisation of anagram-free sequences for graph colorings. A coloring of the vertices of a given graph $G$ is called anagram-free if the sequence of colors on any path in $G$ is anagram-free. We call the minimal number of colors needed for such a coloring the anagram-chromatic number of $G$. In this paper we study the anagram-chromatic number of several classes of graphs like trees, minor-free graphs and bounded-degree graphs. Surprisingly, we show that there are bounded-degree graphs (such as random regular graphs) in which anagrams cannot be avoided unless we basically give each vertex a separate color.

It is shown that a.a.s. as soon as a Kronecker graph becomes connected its diameter is bounded by a constant., Comment: 14 pages

We consider the problem of finding the optimal upper bound for the tail probability of a sum of $k$ nonnegative, independent and identically distributed random variables with given mean $x$. For $k=1$ the answer is given by Markov's inequality and for $k=2$ the solution was found by Hoeffding and Shrikhande in 1955. We solve the problem for $k=3$ as well as for general $k$ and $x\leq1/(2k-1)$ by showing that it follows from the fractional version of an extremal graph theory problem of Erd\H{o}s on matchings in hypergraphs.