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In our previous works, we have studied quantum random walk search algorithm on hypercube, with traversing coin constructed by using generalized Householder reflection and a phase multiplier. When the same phases are used each iteration, the algorithm is robust (stable against errors in the phases) if a certain connection between the phases in the traversing coin is preserved, otherwise small errors lead to poor algorithm performance. Here we investigate how the robustness changes if different phases are used, depending on the current iteration number. We numerically study six different examples with different phase sequences. We show that usage of a particular sequence of phases can make the algorithm more robust even if there is no preserved connection between the phases in the traversing coin., Comment: 28 Pages, 12 Figures, 4 Tables

The article gives the motivations for the measurement of the hyperfine splitting (hfs) in the ground state of muonic hydrogen to explore the properties of the proton at low momentum transfer. It summarizes these proposed measurement methods and finally describes the FAMU experiment in more detail.

We study an opinion dynamics model in which each agent takes a random Bernoulli distributed action whose probability is updated at each discrete time step, and we prove that this model converges almost surely to consensus. We also provide a detailed critique of a claimed proof of this result in the literature. We generalize the result by proving that the assumption of irreducibility in the original model is not necessary. Furthermore, we prove as a corollary of the generalized result that the almost sure convergence to consensus holds also in the presence of a stubborn agent which never changes its opinion. In addition, we show that the model, in both the original and generalized cases, converges to consensus also in $r$th mean., Comment: 15 pages, 9 figures and 1 table. Accepted at IEEE Transactions on Signal and Information Processing over Networks

In this work we study five Grovers algorithm modifications, where each iteration is constructed by two generalized Householder reflections, against inaccuracies in the phases. By using semi-empirical methods, we investigate various characteristics of the dependence between the probability to find solution and the phase errors. The first of them is the robustness of the probability to errors in the phase. The second one is how quickly the probability falls beyond the stability interval. And finally, the average success rate of the algorithm when the parameters are in the range of the highly robust interval. Two of the modifications require usage of the same Grover operator each iteration and in the other three it differs. Those semi-empirical methods give us the, tool to make prediction of the quantum algorithm modifications overall behavior and compare them for even larger register size, Comment: 40 pages, 20 figures, 1 table

The FAMU experiment at RIKEN-RAL is a muonic atom experiment with the aim to determine the Zemach radius of the proton by measuring the 1s hyperfine splitting in muonic hydrogen. The activity of the FAMU Collaboration in the years 2015-2023 enabled the final optimisation of the detector-target setup as well as the gas working condition in terms of temperature, pressure and gas mixture composition. The experiment has started its data taking in July 2023. The status of the detector setup for the 2023 experimental runs, for the beam characterisation and muonic X-ray detection in the 100-200 keV energy range, is presented and discussed., Comment: Submitted to JINST

In January 2020, a workshop was held at EMBL-EBI (Hinxton, UK) to discuss data requirements for deposition and validation of cryoEM structures, with a focus on single-particle analysis. The meeting was attended by 45 experts in data processing, model building and refinement, validation, and archiving of such structures. This report describes the workshop's motivation and history, the topics discussed, and consensus recommendations resulting from the workshop. Some challenges for future methods-development efforts in this area are also highlighted, as is the implementation to date of some of the recommendations., Comment: Outcomes of a wwPDB/EMDB workshop on cryoEM data management, deposition and validation

In this work we study the robustness of two modifications of quantum random walk search algorithm on hypercube. In the first previously suggested modification, on each even iteration only quantum walk is applied. And in the second, the closest neighbors of the solution are measured classically. In our approach the traversing coin is constructed by both generalized Householder reflection and an additional phase multiplier and we investigate the stability of the algorithm to deviations in those phases. We have shown that the unmodified algorithm becomes more robust when a certain relation between those phases is preserved. The first modification we study here does not lead to any change in the robustness of quantum random walk search algorithm. However, when a measurement of the first and second neighbors is included, there are some differences. The most important one, in view of our study of the robustness, is an increase in the stability of the algorithm, especially for large coin dimensions., Comment: 32 pages, 15 figures, 3 tables, 2 Appendices

We report the first experimental determination of the collision-energy dependence of the muon transfer rate from the ground state of muonic hydrogen to oxygen at near-thermal energies. A sharp increase by nearly an order of magnitude in the energy range 0 - 70 meV was found that is not observed in other gases. The results set a reliable reference for quantum-mechanical calculations of low-energy processes with exotic atoms, and provide firm ground for the measurement of the hyperfine splitting in muonic hydrogen and the determination of the Zemach radius of the proton by the FAMU collaboration., Comment: 30 pages, 10 figures

We discuss possible definitions of structural balance conditions in a network with preference orderings as node attributes. The main result is that for the case with three alternatives ($A,B,C$) we reduce the $(3!)^3 = 216$ possible configurations of triangles to $10$ equivalence classes, and use these as measures of balance of a triangle towards possible extensions of structural balance theory. Moreover, we derive a general formula for the number of equivalent classes for preferences on $n$ alternatives. Finally, we analyze a real-world data set and compare its empirical distribution of triangle equivalence classes to a null hypothesis in which preferences are randomly assigned to the nodes., Comment: Accepted for publication in the Asilomar Conference on Signals, Systems and Computers, 2022

This paper examines a way to simplify the circuit of quantum random walk search algorithm, when the traversing coin is constructed by both generalized Householder reflection and an additional phase multiplier. If an appropriate relation between corresponding parameters is realized, our algorithm becomes more robust to deviations in the phases. In this modification marking coin is not needed, and all advantages from above mentioned optimization to the stability, are preserved. It is shown explicitly how to construct such walk coin in order to obtain more robust quantum algorithm., Comment: 11 pages, 6 figures

In this work the quantum random walk search algorithm with walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with arbitrary dimension. Monte Carlo simulations, in combination with supervised machine learning, are used to find walk coins making the quantum algorithm more robust to deviations in the coin's parameters. By applying deep neural network we make prediction for the parameters of an optimal coin with arbitrary size and estimate the stability for such coin., Comment: 31 pages, 19 figures, added two paragraphs and two figures to better explain our results

This paper examines the stability of the quantum random walk search algorithm, when the walk coin is constructed by generalized Householder reflection and additional phase shift, against inaccuracies in the phases used to construct the coin. The optimization of the algorithm is done by numerical methods - Monte Carlo, neural networks, and supervised machine learning. The results of numerical simulations show that, with such a construction of the Householder reflection, the algorithm is more stable to inaccuracies in the specific values of these phases, as long as it is possible to control the phase difference between the phase shift and the phase involved in the Householder reflection. This paper explicitly shows as an example, how achieving a properly designed phase difference would make quantum random walk search on a hypercube more stable for coin register consisting of one, two, and three qubits., Comment: 35 pages, 15 figures, 2 tables, Fixed a typo in Eq.(35)

The first measurement of the temperature dependence of the muon transfer rate from muonic hydrogen to oxygen was performed by the FAMU collaboration in 2016. The results provide evidence that the transfer rate rises with the temperature in the range 104-300 K. This paper presents the results of the experiment done in 2018 to extend the measurements towards lower (70 K) and higher (336 K) temperatures. The 2018 results confirm the temperature dependence of the muon transfer rate observed in 2016 and sets firm ground for comparison with the theoretical predictions.

We study opinion dynamics in a social network with stubborn agents who influence their neighbors but who themselves always stick to their initial opinion. We consider first the well-known DeGroot model. While it is known in the literature that this model can lead to consensus even in the presence of a stubborn agent, we show that the same result holds under weaker assumptions than has been previously reported. We then consider a recent extension of the DeGroot model in which the opinion of each agent is a random Bernoulli distributed variable, and by leveraging on the first result we establish that this model also leads to consensus, in the sense of convergence in probability, in the presence of a stubborn agent. Moreover, all agents' opinions converge to that of the stubborn agent. We also consider a variation on this model where the stubborn agent is replaced with a drifting agent and show that herding is achieved also in this case. Finally, we offer a detailed critique of a proof regarding a claim about a closely related model in the recent literature., Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1912.04183

Molecular hydrogen ions are of metrological relevance due to the possibility of precise theoretical evaluation of their spectrum and of external-field-induced shifts. In homonuclear molecular ions the electric dipole $E1$ transitions are strongly suppressed, and of primary laser spectroscopy interest is the electric quadrupole ($E2$) transition spectrum. In continuation of previous work on the H$_2^+$ ion, we report here the results of the calculations of the hyperfine structure of the laser-induced electric quadrupole transitions between a large set of ro-vibrational states of D$_2^+$; the inaccuracies of previous evaluations have been corrected. The effects of the laser polarization are studied in detail. We show that the electric quadrupole moment of the deuteron can in principle be determined with low fractional uncertainty $(\simeq1\times10^{-4})$ by comparing the results presented here with future data from precision spectroscopy of D$_2^+$., Comment: 19 pages, 4 figures. Comparison with the available experimental data about the hyperfine structure of D2+ has been added in Section IIC; A new Section IIID has been added with a thorough analysis of the determination of the electric quadrupole moment of the deuteron from D2+ spectroscopy; A new Section IIIE has been added discussing further applications of the composite frequency method

We study opinion dynamics in a social network with stubborn agents who influence their neighbors but who themselves always stick to their initial opinion. We consider first the well-known DeGroot model. While it is known in the literature that this model can lead to consensus even in the presence of a stubborn agent, we show that the same result holds under weaker assumptions than has been previously reported. We then consider a recent extension of the DeGroot model in which the opinion of each agent is a random Bernoulli distributed variable, and by leveraging on the first result we establish that this model also leads to consensus, in the sense of convergence in probability, in the presence of a stubborn agent. Moreover, all agents' opinions converge to that of the stubborn agent., Comment: 5 pages; This work was presented at Asilomar Conference on Signals, Systems, and Computers 2019

We report the first measurement of the temperature dependence of muon transfer rate from $\mu$p atoms to oxygen between 100 and 300 K. Data were obtained from the X-ray spectra of delayed events in gaseous target H$_2$/O$_2$ exposed to a muon beam. Based on the data, we determined the muon transfer energy dependence up to 0.1 eV, showing an 8-fold increase in contrast with the predictions of constant rate in the low energy limit. This work set constraints on theoretical models of muon transfer, and is of fundamental importance for the measurement of the hyperfine splitting of $\mu$p by the FAMU collaboration., Comment: 11 pages, 4 figure

This chapter is written for the forthcoming book "A Concise Encyclopedia of Coding Theory" (CRC press), edited by W. Cary Huffman, Jon-Lark Kim, and Patrick Sol\'e. This book will collect short but foundational articles, emphasizing definitions, examples, exhaustive references, and basic facts. The target audience of the Encyclopedia is upper level undergraduates and graduate students., Comment: 22 pages

The main goal of the FAMU experiment is the measurement of the hyperfine splitting (hfs) in the 1S state of muonic hydrogen $\Delta E_{hfs}(\mu^-p)1S$. The physical process behind this experiment is the following: $\mu p$ are formed in a mixture of hydrogen and a higher-Z gas. When absorbing a photon at resonance-energy $\Delta E_{hfs}\approx0.182$~eV, in subsequent collisions with the surrounding $H_2$ molecules, the $\mu p$ is quickly de-excited and accelerated by $\sim2/3$ of the excitation energy. The observable is the time distribution of the K-lines X-rays emitted from the $\mu Z$ formed by muon transfer $(\mu p) +Z \rightarrow (\mu Z)^*+p$, a reaction whose rate depends on the $\mu p$ kinetic energy. The maximal response, to the tuned laser wavelength, of the time distribution of X-ray from K-lines of the $(\mu Z)^*$ cascade indicate the resonance. During the preparatory phase of the FAMU experiment, several measurements have been performed both to validate the methodology and to prepare the best configuration of target and detectors for the spectroscopic measurement. We present here the crucial study of the energy dependence of the transfer rate from muonic hydrogen to oxygen ($\Lambda_{\mu p \rightarrow \mu O}$), precisely measured for the first time., Comment: 11 pages, 4 figures, published on Journal of Physics: Conference Series, proc. of International Conference on Precision Physics of Simple Atomic Systems - PSAS2018. arXiv admin note: text overlap with arXiv:1708.03172

Molecular hydrogen ions are of metrological relevance due to the possibility of precise theoretical evaluation of their spectrum and of external-field-induced shifts. We report the results of the calculations of the rate of laser-induced electric quadrupole transitions between a large set of ro-vibrational states of ${\rm H_2^+}$. The hyperfine and Zeeman structure of the E2 transition spectrum and the effects of the laser polarization are treated in detail. We also present the nuclear spin-electron spin coupling constants, computed with a precision 10 times higher than previously., Comment: 11 pages, 2 figures, 1 supplement

We develop refinements of the Levenshtein bound in $q$-ary Hamming spaces by taking into account the discrete nature of the distances versus the continuous behavior of certain parameters used by Levenshtein. The first relevant cases are investigated in detail and new bounds are presented. In particular, we derive generalizations and $q$-ary analogs of a MacEliece bound. We provide evidence that our approach is as good as the complete linear programming and discuss how faster are our calculations. Finally, we present a table with parameters of codes which, if exist, would attain our bounds.

The FAMU experiment aims to accurately measure the hyperfine splitting of the ground state of the muonic hydrogen atom. A measurement of the transfer rate of muons from hydrogen to heavier gases is necessary for this purpose. In June 2014, within a preliminary experiment, a pressurized gas-target was exposed to the pulsed low-energy muon beam at the RIKEN RAL muon facility (Rutherford Appleton Laboratory, UK). The main goal of the test was the characterization of both the noise induced by the pulsed beam and the X-ray detectors. The apparatus, to some extent rudimental, has served admirably to this task. Technical results have been published that prove the validity of the choices made and pave the way for the next steps. This paper presents the results of physical relevance of measurements of the muon transfer rate to carbon dioxide, oxygen, and argon from non-thermalized excited mu-p atoms. The analysis methodology and the approach to the systematics errors are useful for the subsequent study of the transfer rate as function of the kinetic energy of the mu-p currently under way., Comment: 15 pages, 3 figures, 2 tables

We illustrate the potential of massive MIMO for communication with unmanned aerial vehicles (UAVs). We consider a scenario where multiple single-antenna UAVs simultaneously communicate with a ground station (GS) equipped with a large number of antennas. Specifically, we discuss the achievable uplink (UAV to GS) capacity performance in the case of line-of-sight (LoS) conditions. We develop a realistic geometric model which incorporates an arbitrary orientation of the GS and UAV antenna elements to characterize the polarization mismatch loss which occurs due to the movement and orientation of the UAVs. A closed-form expression for a lower bound on the ergodic rate for a maximum-ratio combining receiver with estimated channel state information is derived. The optimal antenna spacing that maximizes the ergodic rate achieved by an UAV is also determined for uniform linear and rectangular arrays. It is shown that when the UAVs are spherically uniformly distributed around the GS, the ergodic rate per UAV is maximized for an antenna spacing equal to an integer multiple of one-half wavelength., Comment: Accepted for publication in the IEEE Transactions on Wireless Communications

The high precision measurement of the hyperfine splitting of the muonic-hydrogen atom ground state with pulsed and intense muon beam requires careful technological choices both in the construction of a gas target and of the detectors. In June 2014, the pressurized gas target of the FAMU experiment was exposed to the low energy pulsed muon beam at the RIKEN RAL muon facility. The objectives of the test were the characterization of the target, the hodoscope and the X-ray detectors. The apparatus consisted of a beam hodoscope and X-rays detectors made with high purity Germanium and Lanthanum Bromide crystals. In this paper the experimental setup is described and the results of the detector characterization are presented., Comment: 22 pages, 14 figures, published and open access on JINST

Using simulated data, obtained with the FLUKA code, we derive empirical regularities about the propagation and stopping of low-energy negative muons in hydrogen and selected solid materials. The results are intended to help the preliminary stages of the set-up design for experimental studies of muon capture and muonic atom spectroscopy. Provided are approximate expressions for the parameters of the the momentum, spatial and angular distribution of the propagating muons. In comparison with the available data on the stopping power and range of muons (with which they agree in the considered energy range) these results have the advantage to also describe the statistical spread of the muon characteristics of interest., Comment: 17 pages, 9 figures; Version accepted for publication in JINST