Prior investigations of simple rhythms in familiar time signatures have shown the importance of several mechanisms; notably, those related to metricization and grouping. But there has been limited study of complex rhythms, including those in unfamiliar time signatures, such as are found outside mainstream Western music. Here, we investigate how the structures of 91 rhythms with nonisochronous onsets (mostly complex, several in unfamiliar time signatures) influence the accuracy, velocity, and timing of taps made by participants attempting to synchronize with these onsets. The onsets were piano-tone cues sounded at a well-formed subset of isochronous cymbal pulses; the latter occurring every 234 ms. We modelled tapping at both the rhythm level and the pulse level; the latter provides insight into how rhythmic structure makes some cues easier to tap and why incorrect (uncued) taps may occur. In our models, we use a wide variety of quantifications of rhythmic features, several of which are novel and many of which are indicative of underlying mechanisms, strategies, or heuristics. The results show that, for these tricky rhythms, taps are disrupted by unfamiliar period lengths and are guided by crude encodings of each rhythm: the density of rhythmic cues, their circular mean and variance, and recognizing common small patterns and the approximate positions of groups of cues. These lossy encodings are often counterproductive for discriminating between cued and uncued pulses and are quite different to mechanisms-such as metricization and emphasizing group boundaries-thought to guide tapping behaviours in learned and familiar rhythms.

Experiments where participants synchronise their taps to rhythmic cues are often used to study human perception and performance of rhythms. This experimental study is novel in two regards: The cyclic rhythms (non-isochronous patterns of cues) presented to participants were more challenging than usual (including many from unfamiliar time signatures), and we have modelled participants’ performance via a conditional point process. Point processes are well suited to describing partly random sequences of events, but have rarely been used previously to model tapping experiments, the only other study we know being Cannon (2021). Our model uses continuous functional parameters to describe participants’ responses to auditory stimuli with much finer temporal resolution than in previous studies. Taking account of both the clock and the dynamic attention theories of sensorimotor synchronisation, we assessed the time course of the propensity to tap within each cycle at a resolution of less than 13ms, identifying the influence of cues on the tapping propensity and the progress of learning their rhythmic patterns. We also sought to determine the trajectory of the putative refractory period (feedback inhibition of tapping) after each tap, and assessed the distribution of tap-cue asynchronies in a more finely resolved manner than usual. Our models also indicated complex kinetics of the feedback over about 100ms.

Production of relatively few rhythms with non-isochronous beats has been studied. So we assess reproduction of most well-formed looped rhythms comprising K=2-11 cues (a uniform piano tone, indicating where participants should tap) and N=3-13 isochronous pulses (a uniform cymbal). Each rhythm had two different cue interonset intervals. We expected that many of the rhythms would be difficult to tap, because of ambiguous non-isochronous beats and syncopations, and that complexity and asymmetry would predict performance. 111 participants tapped 91 rhythms each heard over 129 pulses, starting as soon as they could. Whereas tap-cue concordance in prior studies was generally >> 90%, here only 52.2% of cues received a temporally congruent tap, and only 63% of taps coincided with a cue. Only −2 ms mean tap asynchrony was observed (whereas for non-musicians this value is usually c. −50 ms). Performances improved as rhythms progressed and were repeated, but precision varied substantially between participants and rhythms. Performances were autoregressive and mixed effects cross-sectional time series analyses retaining the integrity of all the individual time series revealed that performance worsened as complexity features K, N, and cue inter-onset interval entropy increased. Performance worsened with increasing R, the Long: short (L: s) cue interval ratio of each rhythm (indexing both complexity and asymmetry). Rhythm evenness and balance, and whether N was divisible by 2 or 3, were not useful predictors. Tap velocities positively predicted cue fulfilment. Our data indicate that study of a greater diversity of rhythms can broaden our impression of rhythm cognition.

With the increasing popularity of optimization algorithms in electromagnetic engineering, it is clear that mixed-variable design problems prevail. This paper shows that the Cross-Entropy (CE) optimization method is intrinsically versatile to handle these and other types of problems. We provide implementation details of two antenna examples optimized by the CE method to demonstrate its elegance and efficiency.

Broadband antennas find many applications in modern communication systems, such as Wi-Fi, 5G, and SatCom. Multiple competing optimization methods are available for the application to antenna design, while it would be preferable to know in advance if any method is superior. Here, an application of the cross-entropy method, along with particle swarm optimization and covariance matrix adaptation evolutionary strategy, to the design of broadband antennas is presented. The first example is an aperture-coupled microstrip patch antenna that has 9.5 dBi peak directivity and 53% bandwidth after optimization. It is then used as a feed in a high-gain broadband resonant cavity antenna. Using an all-dielectric superstrate with a transverse permittivity gradient, a compact thin resonant cavity antenna with a peak directivity of 19 dBi and 40% 3-dB bandwidth was designed. A comparative analysis of the cross-entropy method, particle swarm optimization, and covariance matrix adaptation evolutionary strategy applied to these two problems was carried out to provide the basis for further optimization of antennas in radio frequency and microwave frequency bands. We found that although all three methods reached a similar solution, the cross-entropy method has a speed advantage. It improves our ability to optimize existing designs and has wider applicability beyond antenna engineering.

Electromagnetic metasurfaces are planar two-dimensional metamaterials, typically of subwavelength thickness. Unit cell elements of different shapes have been widely explored, including electric and magnetic dipoles, patches, arbitrary geometries and pixelated surfaces. Although pixelated metasurfaces have a great advantage of geometric versatility, their design and analysis requires algorithmic approach. One of the techniques for their design is via evolutionary simulation-driven optimization. Since full-wave electromagnetic simulations are time-consuming, optimization methods with fast convergence properties are preferable. In this article, we demonstrate the application of the cross-entropy optimization method to design of artificial magnetic conductors (AMCs) and thin printed phase shifters. Single-frequency AMCs at 10 GHz (X band) and dual-frequency AMCs at 8 and 12 GHz (X and Ku band) were produced that are more manufacturing-friendly, and thus cost effective, than previously reported AMCs. We also show that phase-shifting unit cells with transmission magnitudes over 0.9 (linear) can be designed using the proposed optimization technique. Other potential applications of these unit cells are in phase-correcting and beam-steering metasurfaces.

“We have too many first-year statistics students but too few who choose to major in statistics” is a common complaint among academics in the discipline of statistics, and our department is no exception. Many non-statistics academics appreciate the value of statistics to their discipline and include at least one statistics unit in their required units. However, students in such units often do not see the use of statistics within their discipline or the importance of learning statistics or quantitative skills in general, despite the current shortage of statisticians and deluge of data to be analysed. Our student numbers decline sharply by years of study, from first to second and from second to third. A handful of students who decide to major in statistics or decision science find themselves in high demand. In early 2016, just before the first semester started, we ran an event for the previous year’s successful first-year statistics students to encourage more students to choose statistics or decision science as a second major in addition to their existing majors. We worked with our alumni so that the second-year students heard talks mainly by people like them instead of like us – their lecturers. We called this event ‘Statistics: Your Ticket to Anywhere’. In this paper, we describe how we structured the event, its outcomes for the department, and how it helped us to “unveil the curtain” and to show the value of statistics to the students in their chosen fields of study. First published February 2020 at Statistics Education Research Journal Archives

Strict phase and amplitude control of electromagnetic waves promises significant applications but it still remains a critical challenge. We present a simple, lucid yet versatile stochastic optimization approach to reduce the side-lobe level (SLL) in the radiation pattern of a beam-steering metasurface. The proposed algorithm is capable of efficiently handling computationally expensive electromagnetic (EM) problems. The efficiency of this method has been validated with numerical simulation results, which shows quick and optimal convergence.

An attempt to establish analogy between the antenna array pattern synthesis theory and the metasurface beam-steering control is presented in this paper. Beam steering has been achieved by using a phase transformation metasurface, and the side-lobe level (SLL) reduction has been achieved by optimizing the excitation amplitude of feed array. Optimization has been performed by a simple evolutionary approach based on cross-entropy (CE) method, and the results validate the efficiency of the algorithm, as well as verify the concept of SLL control using excitation amplitude manipulation.

Many real-world electromagnetic design problems are difficult, and their optimisation requires the algorithm to manipulate diverse types of variables and multiple constraints. The cross-entropy (CE) method is a flexible and fast optimisation technique that can be used for optimisation of electromagnetic design problems with mixed variables and multiple constraints. The paper demonstrates the application of the CE method to the design of all-dielectric compact resonant cavity antennas with high gain and wide 3-dB directivity bandwidth and microstrip lowpass filters with high selectivity and wide rejection bandwidth. Both designs incorporate the requirement of fitting the allocated space. The optimised aforementioned designs show further improvement in the performance as compared to the original ones.

Multi-player online esports games are designed for extended durations of play, requiring substantial experience to master. Furthermore, esports game revenues are increasingly driven by in-game purchases. For esports companies, the trends in players leaving their games therefore not only provide information about potential problems in the user experience, but also impacts revenue. Being able to predict when players are about to leave the game - churn prediction - is therefore an important solution for companies in the rapidly growing esports sector, as this allows them to take action to remedy churn problems. The objective of the work presented here is to understand the impact of specific behavioral characteristics on the likelihood of a player continuing to play the esports title League of Legends . Here, a solution to the problem is presented based on the application of survival analysis, using Mixed Effects Cox Regression, to predict player churn. Survival Analysis forms a useful approach for the churn prediction problem as it provides rates as well as an assessment of the characteristics of players who are at risk of leaving the game. Hazard rates are also presented for the leading indicators, with results showing that duration between matches played is a strong indicator of potential churn.

Review of an edited volume covering computational statistical methods in music production, processing, analysis and classification.

Further improvement in the performance of a compact resonant cavity antenna (RCA) with a single planar unprinted superstrate is presented. The RCA design was automated by interfacing the particle swarm optimization (PSO) algorithm with a full-wave solver via scripting. Three benchmark functions were used to assist in the selection of such crucial PSO parameters as population size and maximum number of iterations. The optimal RCA has a peak gain of 19.6 dB, overall 3-dB gain bandwidth of 55% and a small footprint.

Homogeneous Markov chains with discrete state-space and time are very straightforward to simulate, due to the memorylessness property. In this talk, we consider sampling from the normalised restriction of a Markov chains joint distribution to a subset defined by two kinds of constraints: univariate constraints, restricting individual chain variables to belong to certain sets, and multivariate constraints, restricting non-adjacent groups of chain variables to be unequal but equivalent under a predefined equivalence relation. The multivariate constraints, in particular, present some challenges. An efficient sampling method involving Metropolis-Hastings with some pre-tabulated distributions is described. We demonstrate an application to text generation, and in particular the random generation of rhyming, scanning lyrics, as a component of an algorithmic songwriting project. In this setting, the states of the Markov chain are syllables (that know which words they are from, so that for instance the final syllables of perilous and marvellous are two different states). The univariate constraints enforce the metre of the text, by indicating which syllables must be stressed or unstressed (for correct scansion) and which syllables must be word-final (so that words do not straddle lines). The multivariate constraints enforce a rhyming scheme, by requiring certain groups of syllables to rhyme without being equal. This work relies on the Carnegie Mellon Pronouncing Dictionary (CMUdict; Weide, 1998) and sample text. CMUdict contains over 130000 entries, comprising words, proper nouns et cetera as used in spoken American English. This dictionary indicates the phonemic and stress pronunciation of each entry. A Markov chain including the entire dictionary would require over 330000 syllable states. We have used sample texts, both to reduce the state space, and to build a first-order Markov model of word s equence, or equivalently, syllable sequence. The problem of interest is to sample from the Markov chain, subject to the constraints imposed by a given rhyming scheme. Our algorithm firstly samples the multivariately constrained chain variables. After location of a feasible subsequence of rhymed syllables, ratios of joint probabilities are calculated and compared in a Metropolis-Hastings algorithm, where each candidate arises from the incumbent by replacing one set of rhyming syllables with another drawn from a pre-tabulated distribution. After a burn-in period, the skeleton provided by the rhymed syllables is fleshed out by sampling the unrhymed syllables according to the Markov chain, subject to metrical and boundary conditions.

An elegant and simple approach is presented for electromagnetic (EM) optimizations, especially when mixed variables and/or constraints are involved. In mixed-variable optimization, some variables are continuous (can take any value within a range) and others are discrete (can take only values from a database). An example constraint is when the total length of a device under optimization is specified. Our approach can handle such optimization problems and is based on an abstract probabilistic evolutionary optimization algorithm, called the cross-entropy (CE) method. We believe that this is the first application of CE with full-wave EM simulations. A quick performance benchmarking on two test functions was performed to compare convergence of CE and two other established optimization algorithms. Then, the advantages of the CE method when simultaneously optimizing a mix of discrete and continuous variables and imposing geometric constraints are illustrated. Finally, six resonant cavity antennas (RCAs) were optimized, and one was prototyped and tested to verify predicted results. This one-layer-superstrate RCA prototype has a measured peak directivity of 17.6 dBi with a 3 dB directivity bandwidth of 51% and lower sidelobes, outperforming all such prototypes in the literature.

Periodic scales and meters typically embody "organizational principles" - their pitches and onset times are not randomly distributed, but structured by rules or constraints. Identifying such principles is useful for understanding existing music and for generating novel music. In this article, we identify and discuss a novel organizational principle for scales and rhythms that we feel is of both theoretical interest and practical utility: perfect balance. When distributed around the circle. perfectly balanced rhythms and scales have their "centre of gravity" at the centre of the circle. The present article serves as a repository of the theorems and definitions crucial to perfect balance. It also further explores its mathematical ramifications by linking the existing theorems to algebraic number theory and computational optimizations. In the Online Supplement, http://www.dynanuctonality.com/perfect_balance_files/, we provide audio samples of perfectly balanced rhythmic loops and microtonal scales, computational routines, and video demonstrations of some of the concepts.

A Fabry-Perot cavity antenna (FPCA) with extremely wide 3-dB gain bandwidth is presented. Its superstructure consists of a single all-dielectric slab formed from concentric rings with transverse dielectric contrast. The bandwidth enhancement is realized by optimizing permittivity values of the concentric rings using particle swarm optimization. The designed FPCA has a peak gain of 17.6 dB and operates from 10.7 to 22.4 GHz, which is 70% of gain bandwidth.

Optimization of a Fabry-Perot cavity antenna by particle swarm optimization algorithm is presented. The objective of this work was to find the optimal transverse permittivity variation in a planar superstrate providing the maximum directivity bandwidth product. Additionally, a method to reduce the total optimization time is presented. The key antenna parameters of a near-optimal solution, such as peak directivity, 3-dB directivity bandwidth and directivity bandwidth product, are given.

Dmitri Tymoczko describes the voice-leading space of N-note chords as the orbifold T-N/S-N, the N-torus modulo the Nth symmetric group action, "an N-dimensional prism whose simplicial faces are glued together with a twist, and whose remaining boundaries act like mirrors" (2011. A Geometry of Music: Harmony and Counterpoint in the EA-tended Common Practice. Oxford: Oxford University Press). This quotient space T-N/S-N is produced from the space of all ordered sequences of N pitch classes by identifying each sequence with all its reorderings, indicating that we consider a chord unchanged under any permutation of its voices. Here instead we consider a polyphonic setting in which not all voices are free to move independently. Such constraints describe "power chords" in rock (bare fifths or fourths played on guitar) and can also be found in the classical repertoire. We present chord spaces describing excerpts from Bartok and Stravinsky.