RIOT: Recursive Inertial Odometry Transformer for Localisation from Low-Cost IMU Measurements.

Inertial localisation is an important technique as it enables ego-motion estimation in conditions where external observers are unavailable. However, low-cost inertial sensors are inherently corrupted by bias and noise, which lead to unbound errors, making straight integration for position intractable. Traditional mathematical approaches are reliant on prior system knowledge, geometric theories and are constrained by predefined dynamics. Recent advances in deep learning, which benefit from ever-increasing volumes of data and computational power, allow for data-driven solutions that offer more comprehensive understanding. Existing deep inertial odometry solutions rely on estimating the latent states, such as velocity, or are dependent on fixed-sensor positions and periodic motion patterns. In this work, we propose taking the traditional state estimation recursive methodology and applying it in the deep learning domain. Our approach, which incorporates the true position priors in the training process, is trained on inertial measurements and ground truth displacement data, allowing recursion and learning both motion characteristics and systemic error bias and drift. We present two end-to-end frameworks for pose invariant deep inertial odometry that utilises self-attention to capture both spatial features and long-range dependencies in inertial data. We evaluate our approaches against a custom 2-layer Gated Recurrent Unit, trained in the same manner on the same data, and tested each approach on a number of different users, devices and activities. Each network had a sequence length weighted relative trajectory error mean ≤0.4594 m, highlighting the effectiveness of our learning process used in the development of the models.

En route to nanoscopic quantum optical imaging: counting emitters with photon-number-resolving detectors.

The fundamental understanding of biological pathways requires minimally invasive nanoscopic optical resolution imaging. Many approaches to high-resolution imaging rely on localization of single emitters, such as fluorescent molecules or quantum dots. Additionally, the exact determination of the number of such emitters in an imaging volume is essential for a number of applications; however, in standard intensity-based microscopy it is not possible to determine the number of individual emitters within a diffraction limited spot without initial knowledge of system parameters. Here we explore how quantum measurements of the emitted photons using photon number resolving detectors can be used to address this challenging task. In the proposed new approach, the problem of counting emitters reduces to the task of determining differences between the emitted photon distribution and the Poisson limit. We show that quantum measurements of the number of photons emitted from an ensemble of emitters enable the determination of both the number of emitters and the probability of emission. This method can be applied for any type of single-photon emitters. The scaling laws of this new approach are presented by the Cramer-Rao Lower Bounds, and this technique has great potential in quantum optical imaging with nanoscopic resolution.

Preferential coupling of diamond NV centres in step-index fibres.

Diamonds containing the negatively charged nitrogen-vacancy centre are a promising system for room-temperature magnetometry. The combination of nano- and micro-diamond particles with optical fibres provides an option for deploying nitrogen-vacancy magnetometers in harsh and challenging environments. Here we numerically explore the coupling efficiency from nitrogen-vacancy centres within a diamond doped at the core/clad interface across a range of commercially available fibre types so as to inform the design process for a diamond in fibre magnetometers. We determine coupling efficiencies from nitrogen-vacancy centres to the guided modes of a step-index fibre and predict the optically detected magnetic resonance (ODMR) generated by a ensemble of four nitrogen-vacancy centres in this hybrid fibre system. Our results show that the coupling efficiency is enhanced with a high refractive index difference between the fibre core and cladding and depends on the radial position of the nitrogen-vacancy centres in the fibre core. Our ODMR simulations show that due to the preferential coupling of the nitrogen-vacancy emission to the fibre guided modes, certain magnetometry features such as ODMR contrast can be enhanced and lead to improved sensitivity in such diamond-fibre systems, relative to conventional diamond only ensemble geometries.

Einstein, von Frisch and the honeybee: a historical letter comes to light.

The work of the Nobel Laureate Karl von Frisch, the founder of this journal, was seminal in many ways. He established the honeybee as a key animal model for experimental behavioural studies on sensory perception, learning and memory, and first correctly interpreted its famous dance communication. Here, we report on a previously unknown letter by the Physicist and Nobel Laureate Albert Einstein that was written in October 1949. It briefly addresses the work of von Frisch and also queries how understanding animal perception and navigation may lead to innovations in physics. We discuss records proving that Einstein and von Frisch met in April 1949 when von Frisch visited the USA to present a lecture on bees at Princeton University. In the historical context of Einstein's theories and thought experiments, we discuss some more recent discoveries of animal sensory capabilities alien to us humans and potentially valuable for bio-inspired design improvements. We also address the orientation of animals like migratory birds mentioned by Einstein 70 years ago, which pushes the boundaries of our understanding nature, both its biology and physics.

Spontaneous quantity discrimination of artificial flowers by foraging honeybees.

Many animals need to process numerical and quantity information in order to survive. Spontaneous quantity discrimination allows differentiation between two or more quantities without reinforcement or prior training on any numerical task. It is useful for assessing food resources, aggressive interactions, predator avoidance and prey choice. Honeybees have previously demonstrated landmark counting, quantity matching, use of numerical rules, quantity discrimination and arithmetic, but have not been tested for spontaneous quantity discrimination. In bees, spontaneous quantity discrimination could be useful when assessing the quantity of flowers available in a patch and thus maximizing foraging efficiency. In the current study, we assessed the spontaneous quantity discrimination behaviour of honeybees. Bees were trained to associate a single yellow artificial flower with sucrose. Bees were then tested for their ability to discriminate between 13 different quantity comparisons of artificial flowers (numeric ratio range: 0.08-0.8). Bees significantly preferred the higher quantity only in comparisons where '1' was the lower quantity and where there was a sufficient magnitudinal distance between quantities (e.g. 1 versus 12, 1 versus 4, and 1 versus 3 but not 1 versus 2). Our results suggest a possible evolutionary benefit to choosing a foraging patch with a higher quantity of flowers when resources are scarce.

Improved color constancy in honey bees enabled by parallel visual projections from dorsal ocelli.

How can a pollinator, like the honey bee, perceive the same colors on visited flowers, despite continuous and rapid changes in ambient illumination and background color? A hundred years ago, von Kries proposed an elegant solution to this problem, color constancy, which is currently incorporated in many imaging and technological applications. However, empirical evidence on how this method can operate on animal brains remains tenuous. Our mathematical modeling proposes that the observed spectral tuning of simple ocellar photoreceptors in the honey bee allows for the necessary input for an optimal color constancy solution to most natural light environments. The model is fully supported by our detailed description of a neural pathway allowing for the integration of signals originating from the ocellar photoreceptors to the information processing regions in the bee brain. These findings reveal a neural implementation to the classic color constancy problem that can be easily translated into artificial color imaging systems.

Symbolic representation of numerosity by honeybees ( Apis mellifera): matching characters to small quantities.

The assignment of a symbolic representation to a specific numerosity is a fundamental requirement for humans solving complex mathematical calculations used in diverse applications such as algebra, accounting, physics and everyday commerce. Here we show that honeybees are able to learn to match a sign to a numerosity, or a numerosity to a sign, and subsequently transfer this knowledge to novel numerosity stimuli changed in colour properties, shape and configuration. While honeybees learned the associations between two quantities (two; three) and two signs (N-shape; inverted T-shape), they failed at reversing their specific task of sign-to-numerosity matching to numerosity-to-sign matching and vice versa (i.e. a honeybee that learned to match a sign to a number of elements was not able to invert this learning to match the numerosity of elements to a sign). Thus, while bees could learn the association between a symbol and numerosity, it was linked to the specific task and bees could not spontaneously extrapolate the association to a novel, reversed task. Our study therefore reveals that the basic requirement for numerical symbolic representation can be fulfilled by an insect brain, suggesting that the absence of its spontaneous emergence in animals is not due to cognitive limitation.

Modal interferometric refractive index sensing in microstructured exposed core fibres.

Optical fibre-based sensors measuring refractive index shift in bodily fluids and tissues are versatile and accurate probes of physiological processes. Here, we suggest a refractive index sensor based on a microstructured exposed-core fibre (ECF). By considering a high refractive index coating of the exposed core, our modelling demonstrates the splitting of the guided mode into a surface sensing mode and a mode that is isolated from the surface. With the isolated mode acting as a reference arm, this two-mode one-fibre solution provides for robust interferometric sensing with a sensitivity of up to 60, 000 rad/RIU-cm, which is suitable for sensing subtle physiological processes within hard-to-reach places inside living organisms, such as the spinal cord, ovarian tract and blood vessels.

Surpassing the subitizing threshold: appetitive-aversive conditioning improves discrimination of numerosities in honeybees.

Animals including humans, fish and honeybees have demonstrated a quantity discrimination threshold at four objects, often known as subitizing elements. Discrimination between numerosities at or above the subitizing range is considered a complex capacity. In the current study, we trained and tested two groups of bees on their ability to differentiate between quantities (4 versus 5 through to 4 versus 8) when trained with different conditioning procedures. Bees trained with appetitive (reward) differential conditioning demonstrated no significant learning of this task, and limited discrimination above the subitizing range. In contrast, bees trained using appetitive-aversive (reward-aversion) differential conditioning demonstrated significant learning and subsequent discrimination of all tested comparisons from 4 versus 5 to 4 versus 8. Our results show conditioning procedure is vital to performance on numerically challenging tasks, and may inform future research on numerical abilities in other animals.

Synthesis of discrete phase-coherent optical spectra from nonlinear ultrasound.

Nonlinear acoustic interactions in liquids are effectively stronger than nonlinear optical interactions in solids. Thus, harnessing these interactions will offer new possibilities in the design of ultra-compact nonlinear photonic devices. We theoretically demonstrate a new scheme for synthesis of optical spectra from nonlinear ultrasound harmonics using a hybrid liquid-state and nanoplasmonic device compatible with fibre-optic technology. The synthesised spectra consist of a set of equally spaced optical Brillouin light scattering modes having a well-defined phase relationship between each other. We suggest that these spectra may be employed as optical frequency combs whose spectral composition may be tuned by controlling the nonlinear acoustic interactions.

Digital waveguide adiabatic passage part 1: theory.

Spatial adiabatic passage represents a new way to design integrated photonic devices. In conventional adiabatic passage, designs require smoothly varying waveguide separations. Here we show modelling of adiabatic passage devices where the waveguide separation is varied digitally. Despite digitisation, our designs show robustness against variations in the input wavelength and refractive index contrast of the waveguides relative to the cladding. This approach to spatial adiabatic passage opens new design strategies and hence the potential for new photonics devices.

Digital waveguide adiabatic passage part 2: experiment.

Using a femtosecond laser writing technique, we fabricate and characterise three-waveguide digital adiabatic passage devices, with the central waveguide digitised into five discrete waveguidelets. Strongly asymmetric behaviour was observed, devices operated with high fidelity in the counter-intuitive scheme while strongly suppressing transmission in the intuitive. The low differential loss of the digital adiabatic passage designs potentially offers additional functionality for adiabatic passage based devices. These devices operate with a high contrast (>90%) over a 60 nm bandwidth, centered at ∼ 823 nm.

Surface-gate-defined single-electron transistor in a MoS2 bilayer.

We report the multi-scale modeling and design of a gate-defined single-electron transistor in a MoS2 bilayer. By combining density-functional theory and finite-element analysis, we design a surface gate structure to electrostatically define and tune a quantum dot and its associated tunnel barriers in the MoS2 bilayer. Our approach suggests new pathways for the creation of novel quantum electronic devices in two-dimensional materials.

Estimation of the number of single-photon emitters for multiple fluorophores with the same spectral signature.

Fluorescence microscopy is of vital importance for understanding biological function. However most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two, and three otherwise unresolvable fluorophores. The convolution Binomial model is presented to model the counted photons emitted by multiple species. And then the Expectation-Maximization (EM) algorithm is used to match the measured photon counts to the expected convolution Binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced in finding the initial guess of the EM algorithm. Additionally, the associated Cram\'er-Rao lower bound is derived and compared with the simulation results.

Transformation optics for cavity array metamaterials.

Cavity array metamaterials (CAMs), composed of optical microcavities in a lattice coupled via tight-binding interactions, represent a novel architecture for engineering metamaterials. Since the size of the CAMs' constituent elements are commensurate with the operating wavelength of the device, it cannot directly utilise classical transformation optics in the same way as traditional metamaterials. By directly transforming the internal geometry of the system, and locally tuning the permittivity between cavities, we provide an alternative framework suitable for tight-binding implementations of metamaterials. We develop a CAM-based cloak as the case study.

Diamond as a scaffold for bone growth.

Diamond is an attractive material for biomedical implants. In this work, we investigate its capacity as a bone scaffold. It is well established that the bioactivity of a material can be evaluated by examining its capacity to form apatite-like calcium phosphate phases on its surface when exposed to simulated body fluid. Accordingly, polycrystalline diamond (PCD) and ultrananocrystalline diamond (UNCD) deposited by microwave plasma chemical vapour deposition were exposed to simulated body fluid and assessed for apatite growth when compared to the bulk silicon. Scanning electron microscopy and X-ray photoelectron spectroscopy showed that both UNCD and PCD are capable of acting as a bone scaffold. The composition of deposited apatite suggests that UNCD and PCD are suitable for in vivo implantation with UNCD possible favoured in applications where rapid osseointegration is essential.

Single-photon emission and quantum characterization of zinc oxide defects.

Room temperature single-photon emission and quantum characterization is reported for isolated defects in zinc oxide. The defects are observed in thin films of both in-house synthesized and commercial zinc oxide nanoparticles. Emission spectra in the red and infrared, second-order photon correlation functions, lifetime measurements, and photon count rates are presented. Both two- and three-state emitters are identified. Sub-band gap absorption and red emission suggest these defects are the zinc vacancy. These results identify a new source of single photons in a readily available wide band gap semiconductor material which has exceptional electrical, optical, and biocompatibility properties.

Estimation of the number of single-photon emitters for multiple fluorophores with the same spectral signature.

Fluorescence microscopy is of vital importance for understanding biological function. However, most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two and three otherwise unresolvable fluorophores. The convolution binomial model is presented to represent the counted photons emitted by multiple species. Then, the expectation-maximization (EM) algorithm is used to match the measured photon counts to the expected convolution binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced to yield an initial guess for the EM algorithm. Additionally, the associated Cramér-Rao lower bound is derived and compared with the simulation results.