Listener Locations Research Articles

Importance of the receiver's height for transmission studies in acoustic ecology.

In animal communication, the sound pressure level (SPL) of the acoustic signals has been studied in relation to various biological functions. Previous research reported that senders and receivers benefit from being at elevated positions. However, sometimes, researchers find contradictory results. Using a transmission experiment, we measured SPL of two acoustic stimuli: (i) white noise, and (ii) advertisement calls of the Iberian tree frog (Hyla molleri) at two different heights above ground level (0.05 and 0.75 m) and from six distances (1, 2, 4, 8, 16, and 32 m) from a loudspeaker. Calls of the Iberian tree frog have two spectral peaks centred at the frequencies of ca. 1 and 2 kHz. As expected, SPL decreased with distance, but following a distinct attenuation pattern across height above the ground and frequency. Our findings show that the ground effect may critically alter frequency attenuation and, therefore, signal composition and discrimination at the listener's location, even at low heights above the ground. We suggest that recording devices should be positioned at the same height that natural listeners are usually located in nature, to facilitate the replication and comparison of experiments in the field of acoustic ecology and, also, bioacoustics.

Efficient deep learning-based prediction of acoustic parameters in atrium spaces using BIM files

Acoustic simulation tools, although common in the acoustic evaluation of buildings with large atrium space, are costly both in terms of time and resources. This study aims to develop an efficient prediction tool for Reverberation Time (RT) and Sound Pressure Level (SPL) within the atriums using deep learning, with Building Information Modelling (BIM) files as the only input. Initially, a 3-D acoustic simulation model was benchmarked against experimental measurements of RT for an existing building’s atrium, demonstrating an agreement within 15%. Subsequently, BIM files of 60 buildings were used to simulate RT and SPL at various listener locations within their atrium spaces. The BIM files provided essential geometry information, including atrium shape, dimensions, door placements, floor plans, material properties, and sound sources. This dataset was then utilized to train deep learning algorithms, enabling rapid and convenient predictions of RT and SPL for any new building's atrium space. The proposed prediction model serves as a valuable tool for architectural planning and noise regulation during the early design stages. By relying solely on basic building information from the BIM file, this tool obviates the need for time-consuming and computationally expensive simulation software typically used for acoustic evaluations in large atrium spaces.

Effect of speaker orientation on speech intelligibility in an automotive environment

In addition to background noise, binaural effect, and the acoustic boundary conditions of a given space, speech intelligibility (SI) is affected by the source/speaker directivity or orientation, the latter of which has not been researched in small enclosed spaces, such as an automobile. Thus, this study aims to investigate the effect of speaker orientation on SI in automobiles, using both the speech transmission index (STI) and subjective experiments. Given the limited variation range for the orientation of rear-row speakers in an actual scenario, only the situation for front-row speakers was considered in this study. An artificial mouth was regarded as the speaker, which is placed at the driver’s seat. Binaural room impulse responses were measured for different listener locations and speaker orientations in an automobile and a listening room with negligible reflections. Subsequently, STIs were calculated and subjective speech reception thresholds (SRTs) in Mandarin Chinese were evaluated for the different listener locations and speaker orientations. The result shows that the SI in the listening room considerably decreases when the speaker orientation deviates from the listener due to the speaker directivity, with a best-ear STI (SRT) variation of up to 0.24 (7.4 dB). In comparison with the result in the listening room, early reflections improve SI in the automobile by a best-ear STI (SRT) increase (decrease) of up to 0.3 (7.7 dB). The speaker deviating from the listener signifies that the early reflections in the automobile afford a higher SI improvement. Thus, the variation range of SI with various speaker orientations in the automobile was greatly reduced compared with that in the listening room, with a best-ear STI (SRT) variation of no more than 0.1 (2.7 dB). Overall, the speaker orientation mostly does not affect SI except when the speaker is facing the listener due to rich early reflections inside an automobile. Moreover, the comparison between the subjective and objective results shows that the best-ear STI can well express the variation in the SRT in the automobile under various speaker orientations. This study bridges the gap in the research of SI considering various speaker orientations in an automotive environment and helps understand the combined effect of various factors on SI under the special acoustic condition in an automobile.

Wave acoustic solutions in small rooms

This presentation will discuss the growing application of wave based solutions due to the increased processing power of desktop and distributed cloud cluster computing. The causes and mitigation of four types of potential acoustical distortion in small rooms, below and above 200 Hz, will be presented. Below 200 Hz, approaches to minimize modal effects and the speaker boundary interference response will be presented. We will discuss limitations of traditional dimensional ratio determinations, more accurate wave-based predictions, importance of speaker and listener locations, and prediction and measurement of low frequency absorption devices. Above 200 Hz, comb filtering from strong specular reflections and poor diffusion are potential problems. We will describe the necessary ratio of surface width to incident wavelength for a specular reflection and its effect on comb filtering. Finally, we describe the importance of creating a mixing room design and the use of broad bandwidth diffusive surfaces, which can be both measured and simulated with a virtual goniometer boundary element program called VIRGO, from a 3D CAD file topology of any shape. This offers the acoustician the ability to evaluate surface topologies that are of interest in a room design quickly and inexpensively.

Testing listeners' ability to localize virtual sources using sparse loudspeaker arrays and comparison with spherical-head model predictions

Virtual acoustic environments are created by mimicking pressures of real acoustic sources at the ears of a listener. One method to control these pressures is through the use of loudspeaker arrays. While the best results come from arrays with a large number of loudspeakers, they are not practical for everyday use. On the other hand, sparse loudspeaker arrays are physically limited by the listener's localization ability and the sensitivity to head translation and rotation. Previously a model was created to find the limits of each of these features for a spherical head in a free-field environment. Subsequently the loudspeaker locations were optimized based on these features. Listening tests were carried out to find the limits of these features for a variety of loudspeaker array configurations. These tests were carried out in an anechoic chamber with the loudspeaker locations hidden by acoustically transparent curtains. The localization ability for each configuration was recorded. This was repeated for deviations from the optimal listener location in both head rotation and translation. The results were compared to the free-field model previously established.

P078 Delivering far reaching patient education in rheumatological conditions and treatments: RadioRheumatology podcasts

Background/Aims There is a need for accessible rheumatic patient education . Podcasts can be accessed globally, are simple and cheap to produce and enable access by patients who may have reading difficulties. They also allow local patients to connect personally with their rheumatology department staff. Hospital radio departments offer access to high quality recording equipment and often have spare capacity to facilitate recordings Methods RadioRheumatology podcasts are recorded by our rheumatology clinical team with technical support from RadioFrimleyPark volunteers.Hospital radio departments are often under-utilised and have enthusiastic volunteers. The podcasts are uploaded to our podcast hosting website Buzzsprout (accessible at www.rheumatology.buzzsprout.com) and then propagated to Spotify, Apple Podcasts, Android Podcasts and other podcasts sites. Listeners can find our episodes via social media platforms or by searching their podcast provider of choice. We offer a 'QR' link to the podcasts for our patients in clinic and can send the link in a letter or email. In the last 11 months we have recorded podcasts on 'Steroids in Rheumatology', 'Methotrexate Overview' 'Early Inflammatory Arthritis' and 'Rheumatoid Arthritis'. Results RadioRheumatology has been received well both locally and internationally with listeners in 62 different countries. Statistical data is sent from the podcast website on a monthly basis including 'top episodes', 'top apps', listener locations and devices used (to listen to the podcasts): The 'Methotrexate' episode has been the most popular to date and has had over 550 listeners at the time of writing.The United Kingdom has had the most 'listens' (570) followed by The United States (428). We have had listeners as far afield as New Zealand and Malaysia. Within the UK Islington,had the most listens (105), followed by Blackheath (91) Apple iPhone is the most commonly used device used to access (with 694 listens). Feedback so far has been positive.We have have had 5 star reviews and positive feedback from both patients and healthcare professionals. 5* review: A very easy to understand guide to RA: “Fantastic podcast which really explains rheumatoid arthritis but more importantly the help and support available to patients. As a Biologic Specialist Nurse I will certainly be directing my patients and families to this podcast to help them manage their conditions effectively" Conclusion Podcasts can be an effective and cost-effective way to deliver patient education They enable both local and wider patient contact. Podcasts are an increasingly popular medium, particularly since the advent of COVID-19; listener number feedback and reviews enable us to assess the popularity of our episodes and tailor future podcasts accordingly. Hospital radio volunteers have been central to the success of this project by offering their time and championing the use of hospital radio to support clinical teams in delivering patient education. Disclosure R.M. Killick: None. J. Cameron: None. S. Smith: None. M. Lloyd: None. J. Wajed: None.

Objective Assessment of Speech Intelligibility in Crowded Public Spaces.

The objective of this study was to obtain a normative database of speech intelligibility data for young normal-hearing listeners communicating in public spaces. A total of 174 listeners participated in an interactive speech intelligibility task that required four-person groups to conduct a live version of the Modified Rhyme Test in noisy public spaces. The public spaces tested included a college library, a college cafeteria, a casual dining restaurant during lunch hour, and a crowded bar during happy hour. At the start of each trial, one of the participants was randomly selected as the talker, and a tablet computer was used to prompt them to say a word aloud from the Modified Rhyme Test. Then, the other three participants were required to select this word from one of six rhyming alternatives displayed on three other tablet computers. The tablet computers were also used to record the SPL at each listener location during and after the interval where the target talker was speaking. These SPL measurements were used to estimate the signal-to-noise ratio (SNR) in each trial of the experiment. As expected, the results show that speech intelligibility decreases, response time increases, and perceived difficulty increases as the background noise level increases. There was also a systematic decrease in SNR with increasing background noise, with SNR decreasing 0.44 dB for every 1 dB increase in ambient noise level above 60 dB. Overall, the results of this study have demonstrated how low-cost tablet computer-based data collection systems can be used to collect live-talker speech intelligibility data in real-world environments. We believe these techniques could be adapted for use in future studies focused on obtaining ecologically valid assessments of the effects of age, hearing impairment, amplification, and other factors on speech intelligibility performance in real-world environments.

Acoustic texture rendering for extended sources in complex scenes

Extended stochastic sources, like falling rain or a flowing waterway, provide an immersive ambience in virtual environments. In complex scenes, the rendered sound should vary naturally with listener position, differing not only in overall loudness but also in texture, to capture the indistinct murmur of a faraway brook versus the bright babbling of one up close. Modeling an ambient sound as a collection of random events such as individual raindrop impacts or water bubble oscillations, this variation can be seen as a change in the statistical distribution of events heard by the listener: the arrival rate of nearby, louder events relative to more distant or occluded, quieter ones. Reverberation and edge diffraction from scene geometry multiply and mix events more extensively compared to an empty scene and introduce salient spatial variation in texture. We formalize the notion of acoustic texture by introducing the event loudness density (ELD), which relates the rapidity of received events to their loudness. To model spatial variation in texture, the ELD is made a function of listener location in the scene. We show that this ELD field can be extracted from a single wave simulation for each extended source and rendered flexibly using a granular synthesis pipeline, with grains derived procedurally or from recordings. Our system yields believable, realtime changes in acoustic texture as the listener moves, driven by sound propagation in the scene.

Adaptive Sampling for Sound Propagation.

Precomputed sound propagation samples acoustics at discrete scene probe positions to support dynamic listener locations. An offline 3D numerical simulation is performed at each probe and the resulting field is encoded for runtime rendering with dynamic sources. Prior work place probes on a uniform grid, requiring high density to resolve narrow spaces. Our adaptive sampling approach varies probe density based on a novel "local diameter" measure of the space surrounding a given point, evaluated by stochastically tracing paths in the scene. We apply this measure to layout probes so as to smoothly adapt resolution and eliminate undersampling in corners, narrow corridors and stairways, while coarsening appropriately in more open areas. Coupled with a new runtime interpolator based on radial weights over geodesic paths, we achieve smooth acoustic effects that respect scene boundaries as both the source or listener move, unlike existing visibility-based solutions. We consistently demonstrate quality improvement over prior work at fixed cost.

Ambient sound propagation

Ambient sounds arise from a massive superposition of chaotic events distributed over a large area or volume, such as waves breaking on a beach or rain hitting the ground. The directionality and loudness of these sounds as they propagate in complex 3D scenes vary with listener location, providing cues that distinguish indoors from outdoors and reveal portals and occluders. We show that ambient sources can be approximated using an ideal notion of spatio-temporal incoherence and develop a lightweight technique to capture their global propagation effects. Our approach precomputes a single FDTD simulation using a sustained source signal whose phase is randomized over frequency and source extent. It then extracts a spherical harmonic encoding of the resulting steady-state distribution of power over direction and position in the scene using an efficient flux density formulation. The resulting parameter fields are smooth and compressible, requiring only a few MB of memory per extended source. We also present a fast binaural rendering technique that exploits phase incoherence to reduce filtering cost.

Potential audibility of ultrasonic signal monitoring of Public Address and Life Safety Sound Systems.

Ultrasonic surveillance monitoring, to check the operational integrity of Public Address (PA) and Emergency Communication Systems, has been in existence for over 40 years-particularly in Europe. Since its inception, there has been debate as to the potential audibility that these systems may have. As the vast majority of sound systems engineers and designers have not heard or experienced any effects, it has generally been assumed that the general public do not either. Recently, however, concern has been raised and claims of ill effects have been reported with respect to ultrasonic emissions. There is, however, little or no data as to the ultrasonic sound levels that sound systems actually emit. This paper discusses the results of an initial survey of ultrasound radiated by a sample of some 50 sound systems and compares the results with a number of international standards-there currently being little or no specific guidance. This paper reviews the technology involved, typical emission levels, and concludes by making a number of recommendations to assist with the control of ultrasonic emissions to help mitigate unintended side effects. It is shown that most PA systems generate ultrasonic levels of under 70 dB at normal listener locations.

Parametric directional coding for precomputed sound propagation

Convincing audio for games and virtual reality requires modeling directional propagation effects. The initial sound's arrival direction is particularly salient and derives from multiply-diffracted paths in complex scenes. When source and listener straddle occluders, the initial sound and multiply-scattered reverberation stream through gaps and portals, helping the listener navigate. Geometry near the source and/or listener reveals its presence through anisotropic reflections. We propose the first precomputed wave technique to capture such directional effects in general scenes comprising millions of polygons. These effects are formally represented with the 9D directional response function of 3D source and listener location, time, and direction at the listener, making memory use the major concern. We propose a novel parametric encoder that compresses this function within a budget of ~100MB for large scenes, while capturing many salient acoustic effects indoors and outdoors. The encoder is complemented with a lightweight signal processing algorithm whose filtering cost is largely insensitive to the number of sound sources, resulting in an immediately practical system.

Challenges of entertainment sound in communities

There are three basic challenges of entertainment sound in communities. First is how to measure the sound. People often clearly hear individual notes of music being played, individual beats from drums, and other lower frequency percussive instruments and sounds of words sung by performers at locations away from the facility. Equivalent sound levels taken over varying periods of time, LA Fast, LA slow, and other experimental metrics will be compared with the audibility of the sounds by people at remote listening locations. Second, it is often necessary to correct the measurements for the effects of background noise when equivalent sound levels are measured because the short term transient sounds that contain the musical information have been “averaged away” and the resulting sound levels are in the vicinity of the background sounds even though the words and music are plainly audible. Third is that methods to effectively contain the sounds from outdoor amplified entertainment facilities including operational controls, infrastructure controls, and administrative controls should be considered. All three challenges must be addressed to optimize the compatibility of the facility with the community.

Listening to War: Sound, Music, Trauma, and Survival in Wartime Iraq by J. Martin Daughtry

Reviewed by: Listening to War: Sound, Music, Trauma, and Survival in Wartime Iraq by J. Martin Daughtry Sarah J. Dietsche Listening to War: Sound, Music, Trauma, and Survival in Wartime Iraq. By J. Martin Daughtry. New York: Oxford University Press, 2015. [ 344 p. ISBN 9780199361496 (hardcover). $29.95; ISBN 9780199361526 (e-book), varies.] Notes, glossary, bibliography, index. The Iraq War and the ongoing conflicts in the Middle East are among the most controversial topics in modern American society. Soldiers return changed—if not physically wounded, often with mental or emotional scars. Some of these wounds—most notably, Post-Traumatic Stress Disorder, or the signature injury of the Iraq War, Traumatic Brain Injury—were created not by shrapnel or bullets, but by the sounds of war. In Listening to War: Sound, Music, Trauma, and Survival in Wartime Iraq, J. Martin Daughtry addresses not only the wounds that belliphonic sounds (a term coined by Daughtry to describe the spectrum of sounds produced by armed combat) can create but also the ways in which sounds were experienced and used by soldiers, Iraqi civilians, and insurgents during the war. It is worth noting that the term "war" in this case does not fit a strict definition, but Daughtry's research documents the period beginning with the initial Shock and Awe campaign (March 21, 2003) through the end of 2011, when the last foreign combat troops left Iraq. Daughtry's main argument in Listening to War is that belliphonic sounds have measurable physiological and psychological effects on listeners, and that those effects differ greatly based on the divergent experiences of auditors. The listener's location, cultural background, role as participant or observer, etc., all affect these experiences. Daughtry compares and contrasts these effects with those of sounds that are heard during normal life (in America or Iraq) as well as those produced during other conflicts. J. Martin Daughtry is an Associate Professor of Music at New York University. His work has had a preoccupation with violence from the start. One of his earliest projects—and his best-known publication—was the volume that he co-edited with Jonathan Ritter, Music in the Post 9/11 World (New York: Routledge, 2007), which explored how 9/11 shaped music in the United States and around the globe. In addition to his work in music and sound related to the post-9/11 era, he also studies music and violence in Russia. Situated within the field of ethnomusicology, his work focuses on music and politics, acoustic violence, and sound studies. There has been a fair amount of music research that was produced in reaction to the Iraq War (including Daughtry's own co-edited volume mentioned above; Chris Willman, Rednecks and Bluenecks: The Politics of Country Music [New York: The New Press, 2005]; Sarah J. Dietsche, "Sound Divide: American Popular Music's Response to the [End Page 67] 'War on Terror' During the George W. Bush Administration," [Ph.D. diss., The University of Memphis, 2016]), as well as research on music that the soldiers heard, used, and produced during the war (Jonathan R. Pieslak, Sound Targets: American Soldiers and Music in the Iraq War [Bloomington, IN: Indiana University Press, 2009]), but Daughtry's book explores this era in a different way. He discusses the actual sounds of bullets, explosions, and other common belliphonic sounds, and draws on techniques from the field of sound studies. Originating from John Cage's questions about how sounds from plants, white noise, and even blood pumping through our own veins can be experienced and influence us, the field of sound studies began in earnest in the 1990s and was largely codified in Jonathan Sterne's The Audible Past: Cultural Origins of Sound Reproduction (Durham, NC: Duke University Press, 2003). The section headings of Sterne's book, The Sound Studies Reader (New York: Routledge, 2012), outline the six main areas of sound studies: Hearing, Listening, Deafness; Spaces, Sites, Scapes; Transduce and Record; Collectivities and Couplings; Aesthetics, Experiences, Interpretation; and Voices. In Listening to War, Daughtry addresses many of these subjects, and his work continues to define this evolving research area. The first chapter focuses on the actual sounds experienced during the Iraq War. Daughtry...

The impact of architecture on both the intelligibility and privacy of speech

Architects design the “visual space” that we can all see, and this we call architecture. Acousticians upon entering this visual space invariably clap their hands, and as such are assessing the resulting “aural space.” Acoustics is the result of architecture, and so, speech clarity is determined by architecture—meaning the size, shape, and surface treatments chosen by the architect to deliver the mission for which the space is intended. We can look at (model) or listen to (field evaluate) the impulse response of a room, and from this determine the degree of speech clarity that is projected to any listening location. Designing for good speech intelligibility within a space means providing adequate speech clarity and then protecting this signal with a high signal-to-noise ratio (S/N) to ensure that the signal can be heard above the ambient noise. If on the other hand we seek to limit the speech intelligibility (privacy) between spaces, we need to design the architecture to limit the intrusion of speech between spaces taking into consideration the architectural choices as barriers to sound transmission via walls, ceilings, and floors. Examples of design approaches in both cases of intelligibility and privacy will be shown.

The role of location in everyday experiences of music.

Mehrabian and Russell’s (1974) Pleasure–Arousal–Dominance model states that a propensity to approach/avoid an environment can be conceptualized in terms of the pleasure and arousal it elicits and one’s degree of dominance therein. Using the Experience Sampling Method, 177 individuals provided responses concerning Mehrabian and Russell’s model throughout 1 wk regarding music experiences that occurred in their daily life (including how the music was heard and how their responses related to the listening location). Results indicate that the time of day and day of week are related to where music is experienced, and that the consequences of what was heard are related to both time and location. Although music was experienced more often in private locations than in public overall, interesting patterns of music experiences that occurred in public locations demonstrate in detail how music listening varies by location. Specifically, portable devices were associated with positive responses, which contrasted sharply with the responses to music broadcasted publicly in public settings. Participants’ ratings of choice, liking, and arousal demonstrated the importance of considering choice as an indication of dominance, such that music usage is consistent with Mehrabian and Russell’s model, and has functions that vary according to the specific characteristics of the situation.

Interactive Acoustic Transfer Approximation for Modal Sound

Current linear modal sound models are tightly coupled with their frequency content. Both the modal vibration of object surfaces and the resulting sound radiation depend on the vibration frequency. Whenever the user tweaks modal parameters to adjust frequencies the modal sound model changes completely, necessitating expensive recomputation of modal vibration and sound radiation. We propose a new method for interactive and continuous editing as well as exploration of modal sound parameters. We start by sampling a number of key points around a vibrating object, and then devise a compact, low-memory representation of frequency-varying acoustic transfer values at each key point using Prony series. We efficiently precompute these series using an adaptive frequency sweeping algorithm and volume-velocity-preserving mesh simplification. At runtime, we approximate acoustic transfer values using standard multipole expansions. Given user-specified modal frequencies, we solve a small least-squares system to estimate the expansion coefficients, and thereby quickly compute the resulting sound pressure value at arbitrary listening locations. We demonstrate the numerical accuracy, the runtime performance of our method on a set of comparisons and examples, and evaluate sound quality with user perception studies.

Development of hearing protection device calculators for the F-35A and F-35B tactical aircraft

Simple spreadsheet-based near field noise prediction tools for the F-35A (conventional takeoff and landing) and F-35B (short takeoff and vertical landing) aircraft have been developed recently. Near field noise predictions are based on empirical data collected during static engine runs conducted at Edwards AFB, and during hover/vertical landing operations at MCAS Yuma in September, 2013. The tools are programmed to calculate near field one-third octave band sound pressure levels as a function of engine power setting and listener location. The calculated near field levels can be used to determine the Total Daily Exposure (TDE) of personnel required to work in the vicinity of powered aircraft. Alternatively, the calculators can be used to determine the amount of hearing protection required so that the personnel TDEs remain below 1.0. The calculators are adjustable so that they can be employed for differing domestic and international noise exposure regulations. [Work supported by the Air Force Research Laboratory and Ball Aerospace.]

The role of amplitude modulation in auditory distance perception

The ratio of direct to reverberant sound energy (D/R) has been shown to be a primary acoustic cue to perceived sound source distance. Because it is unclear exactly how D/R might be encoded in the auditory system, a variety of more physiologically plausible correlates to D/R have been identified, including: spectral variance, interaural correlation, and temporal cues. Here, following recent neural work by Kuwada and Kim [ARO (2014)], we describe a new correlate to D/R and perceived distance related to the amplitude modulation (AM) depth of the signal at the listener's location. This cue is caused by the change in the modulation transfer characteristics of the room as a function of source distance. Results from an apparent distance estimation task confirm the efficacy of this AM depth cue in a reverberant soundfield (approximate broadband T60 = 3 s), when level cues are made ineffective. Distance estimates were found to be more accurate when the source signal (1-octave band of noise centered at 4 kHz) had AM (32 Hz, 100% depth), and this facilitation was only observed in reverberation. The facilitation was most evident for monaural input, indicating that the AM depth cue is likely processed monaurally.

Real-time sound propagation and noise modeling in outdoor environments using Equivalent Source Formulation

We address the problem of wave-based sound propagation in outdoor and urban environments. The goal is to accurately simulate acoustic effects, including interference, diffraction, scattering, and higher-order wave effects in large outdoor scenes. We give an overview of a precomputed wave-based solver that is based on equivalent source method and is mainly applicable to large, open scenes [Mehra et al. 2012]. As part of a preprocessing step, it computes a per-object transfer function that models the scattering behavior of each object, and handles pair-wise acoustic coupling between objects using inter-object transfer functions. The runtime component involves fast summation over all outgoing equivalent sources for all objects at the listener location. We highlight its runtime performance and memory efficiency and use it for noise modeling and prediction in outdoor scenes spanning a few hundreds of meters. The sound field is computed in three dimensions, modeling frequency-dependent propagation above ceilings, around buildings and corners, and high-order interactions.