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The feasibility of variational quantum algorithms, the most popular correspondent of neural networks on noisy, near-term quantum hardware, is highly impacted by the circuit depth of the involved parametrized quantum circuits (PQCs). Higher depth increases expressivity, but also results in a detrimental accumulation of errors. Furthermore, the number of parameters involved in the PQC significantly influences the performance through the necessary number of measurements to evaluate gradients, which scales linearly with the number of parameters. Motivated by this, we look at deep equilibrium models (DEQs), which mimic an infinite-depth, weight-tied network using a fraction of the memory by employing a root solver to find the fixed points of the network. In this work, we present Quantum Deep Equilibrium Models (QDEQs): a training paradigm that learns parameters of a quantum machine learning model given by a PQC using DEQs. To our knowledge, no work has yet explored the application of DEQs to QML models. We apply QDEQs to find the parameters of a quantum circuit in two settings: the first involves classifying MNIST-4 digits with 4 qubits; the second extends it to 10 classes of MNIST, FashionMNIST and CIFAR. We find that QDEQ is not only competitive with comparable existing baseline models, but also achieves higher performance than a network with 5 times more layers. This demonstrates that the QDEQ paradigm can be used to develop significantly more shallow quantum circuits for a given task, something which is essential for the utility of near-term quantum computers. Our code is available at https://github.com/martaskrt/qdeq., Comment: To be published in NeurIPS 2024

This paper presents the syntax and reduction rules for an abstract machine based on the JavaScript XML language. We incorporate the notion of cost into our reduction rules, and create a type system that over-approximate this cost. This over-approximation results in an equation that may contain unknowns originating from while loops. We conclude with a formal proof of soundness of the type system for our abstract machine, demonstrating that it over-approximates the cost of any terminating program. An implementation of the type system, constraint gathering, and the abstract machine is also presented, Comment: Benjamin Bennetzen: 0009-0007-1751-6862 Daniel Vang Kleist: 0009-0005-1785-2124 Emilie Sonne Steinmann: 0009-0000-4733-5842 Loke Walsted: 0009-0002-1758-4594 Nikolaj Rossander Kristensen: 0009-0005-2339-8247 Peter Buus Steffensen: 0009-0005-6410-5869

Protecting confidential data from leaking is a critical challenge in computer systems, particularly given the growing number of observers on the internet. Therefore, limiting information flow using robust security policies becomes increasingly vital. We focus on the non-interference policy, where the goal is to ensure that confidential data can not impact public data. This paper presents a type system, for a subset of the ReScript syntax, designed to enforce non-interference. We conclude with a proof of soundness for the type system, demonstrating that if an expression is type-able, it is inherently non-interferent. In addition, we provide a brief overview of a type checker that implements the previously mentioned type system., Comment: Benjamin Bennetzen: 0009-0007-1751-6862 Daniel Vang Kleist: 0009-0005-1785-2124 Emilie Sonne Steinmann: 0009-0000-4733-5842 Loke Walsted: 0009-0002-1758-4594 Nikolaj Rossander Kristensen: 0009-0005-2339-8247 Peter Buus Steffensen: 0009-0005-6410-5869

Does the People's Republic of China (PRC) interfere with European elections through ethnic Chinese diaspora media? This question forms the basis of an ongoing research project exploring how PRC narratives about European elections are represented in Chinese diaspora media, and thus the objectives of PRC news media manipulation. In order to study diaspora media efficiently and at scale, it is necessary to use techniques derived from quantitative text analysis, such as topic modelling. In this paper, we present a pipeline for studying information dynamics in Chinese media. Firstly, we present KeyNMF, a new approach to static and dynamic topic modelling using transformer-based contextual embedding models. We provide benchmark evaluations to demonstrate that our approach is competitive on a number of Chinese datasets and metrics. Secondly, we integrate KeyNMF with existing methods for describing information dynamics in complex systems. We apply this pipeline to data from five news sites, focusing on the period of time leading up to the 2024 European parliamentary elections. Our methods and results demonstrate the effectiveness of KeyNMF for studying information dynamics in Chinese media and lay groundwork for further work addressing the broader research questions., Comment: Accepted to the 2024 Computational Humanities Research Conference (CHR)

Metaphors are everywhere. They appear extensively across all domains of natural language, from the most sophisticated poetry to seemingly dry academic prose. A significant body of research in the cognitive science of language argues for the existence of conceptual metaphors, the systematic structuring of one domain of experience in the language of another. Conceptual metaphors are not simply rhetorical flourishes but are crucial evidence of the role of analogical reasoning in human cognition. In this paper, we ask whether Large Language Models (LLMs) can accurately identify and explain the presence of such conceptual metaphors in natural language data. Using a novel prompting technique based on metaphor annotation guidelines, we demonstrate that LLMs are a promising tool for large-scale computational research on conceptual metaphors. Further, we show that LLMs are able to apply procedural guidelines designed for human annotators, displaying a surprising depth of linguistic knowledge., Comment: Accepted to the 2024 Computational Humanities Research Conference (CHR)

Focalization, the perspective through which narrative is presented, is encoded via a wide range of lexico-grammatical features and is subject to reader interpretation. Moreover, trained readers regularly disagree on interpretations, suggesting that this problem may be computationally intractable. In this paper, we provide experiments to test how well contemporary Large Language Models (LLMs) perform when annotating literary texts for focalization mode. Despite the challenging nature of the task, LLMs show comparable performance to trained human annotators in our experiments. We provide a case study working with the novels of Stephen King to demonstrate the usefulness of this approach for computational literary studies, illustrating how focalization can be studied at scale.

We investigate the emergence of stable subspaces in the low-temperature quantum thermal dynamics of finite spin chains. Our analysis reveals the existence of effective decoherence-free qudit subspaces, persisting for timescales exponential in $\beta$. Surprisingly, the appearance of metastable subspaces is not directly related to the entanglement structure of the ground state(s). Rather, they arise from symmetry relations in low-lying excited states. Despite their stability within a 'phase', practical realization of stable qubits is hindered by susceptibility to symmetry-breaking perturbations. This work highlights that there can be non-trivial quantum behavior in the thermal dynamics of noncommuting many body models, and opens the door to more extensive studies of self-correction in such systems.

Faithful quantum state transfer between telecom photons and microwave frequency mechanical oscillations necessitate a fast conversion rate and low thermal noise. Two-dimensional (2D) optomechanical crystals (OMCs) are favorable candidates that satisfy those requirements. 2D OMCs enable sufficiently high mechanical frequency (1$\sim$10 GHz) to make the resolved-sideband regime achievable, a prerequisite for many quantum protocols. It also supports higher thermal conductance than 1D structures, mitigating the parasitic laser absorption heating. Furthermore, gallium phosphide (GaP) is a promising material choice thanks to its large electronic bandgap of 2.26 eV, which suppresses two-photon absorption, and high refractive index $n$ = 3.05 at the telecom C-band, leading to a high-$Q$ optical mode. Here, we fabricate and characterize a 2D OMC made of GaP. We realize a high optical $Q$-factor of $7.9\times 10^{4}$, corresponding to a linewidth $\kappa/2\pi$ = 2.5 GHz at the telecom frequency 195.6 THz. This optical mode couples to several mechanical modes, whose frequencies all exceed the cavity linewidth. The most strongly coupled mode oscillates at 7.7 GHz, more than 3 times the optical linewidth, while achieving a substantial vacuum optomechanical coupling rate $g_{\mathrm{0}}/2\pi$ = 450 kHz. This makes the platform a promising candidate for a long-lived, deterministic quantum memory for telecom photons at low temperatures.

Topological insulators were originally discovered for electron waves in condensed matter systems. Recently this concept has been transferred to bosonic systems such as photons and phonons, which propagate in materials patterned with artificial lattices that emulate spin-Hall physics. This work has been motivated, in part, by the prospect of topologically protected transport along edge channels in on-chip circuits. Importantly, even in principle, topology protects propagation against backscattering, but not against loss, which has remained limited to the dB/cm-level for phonon waveguides, be they topological or not. Here, we combine advanced dissipation engineering, in particular the recently introduced method of soft-clamping, with the concept of a valley-Hall topological insulator for phonons. This enables on-chip phononic waveguides with propagation losses of 3 dB/km at room temperature, orders of magnitude below any previous chip-scale devices. For the first time, the low losses also allow us to accurately quantify backscattering protection in a topological phonon waveguide, using high-resolution ultrasound spectroscopy. We infer that phonons follow a sharp, 120 degree-bend with a 99.99%-probability instead of being scattered back, and less than one phonon in a million is lost. The extraordinary combination of features of this novel platform suggest applications in classical and quantum signal routing, processing, and storage., Comment: Main manuscript (16 pages, 4 figures) and supplementary information (19 pages, 10 figures)

Marine in-situ data is collected by sensors mounted on fixed or mobile systems deployed into the ocean. This type of data is crucial both for the ocean industries and public authorities, e.g., for monitoring and forecasting the state of marine ecosystems and/or climate changes. Various public organizations have collected, managed, and openly shared in-situ marine data in the past decade. Recently, initiatives like the Ocean Decade Corporate Data Group have incentivized the sharing of marine data of public interest from private companies aiding in ocean management. However, there is no clear understanding of the impact of data quality in the engineering of systems, as well as on how to manage and exploit the collected data. In this paper, we propose main architectural decisions and a data flow-oriented component and connector view for marine in-situ data streams. Our results are based on a longitudinal empirical software engineering process, and driven by knowledge extracted from the experts in the marine domain from public and private organizations, and challenges identified in the literature. The proposed software architecture is instantiated and exemplified in a prototype implementation., Comment: The paper is accepted at the 21st IEEE International Conference on Software Architecture (ICSA 2024)

The rapid advancements in artificial intelligence, big data analytics, and cloud computing have precipitated an unprecedented demand for computational resources. However, the current landscape of computational resource allocation is characterized by significant inefficiencies, including underutilization and price volatility. This paper addresses these challenges by introducing a novel global platform for the commodification of compute hours, termed the Global Compute Exchange (GCX) (Patent Pending). The GCX leverages blockchain technology and smart contracts to create a secure, transparent, and efficient marketplace for buying and selling computational power. The GCX is built in a layered fashion, comprising Market, App, Clearing, Risk Management, Exchange (Offchain), and Blockchain (Onchain) layers, each ensuring a robust and efficient operation. This platform aims to revolutionize the computational resource market by fostering a decentralized, efficient, and transparent ecosystem that ensures equitable access to computing power, stimulates innovation, and supports diverse user needs on a global scale. By transforming compute hours into a tradable commodity, the GCX seeks to optimize resource utilization, stabilize pricing, and democratize access to computational resources. This paper explores the technological infrastructure, market potential, and societal impact of the GCX, positioning it as a pioneering solution poised to drive the next wave of innovation in commodities and compute.

Insect production for food and feed presents a promising supplement to ensure food safety and address the adverse impacts of agriculture on climate and environment in the future. However, optimisation is required for insect production to realise its full potential. This can be by targeted improvement of traits of interest through selective breeding, an approach which has so far been underexplored and underutilised in insect farming. Here we present a comprehensive review of the selective breeding framework in the context of insect production. We systematically evaluate adjustments of selective breeding techniques to the realm of insects and highlight the essential components integral to the breeding process. The discussion covers every step of a conventional breeding scheme, such as formulation of breeding objectives, phenotyping, estimation of genetic parameters and breeding values, selection of appropriate breeding strategies, and mitigation of issues associated with genetic diversity depletion and inbreeding. This review combines knowledge from diverse disciplines, bridging the gap between animal breeding, quantitative genetics, evolutionary biology, and entomology, offering an integrated view of the insect breeding research area and uniting knowledge which has previously remained scattered across diverse fields of expertise.

(abridged) Protostellar outflows exhibit large variations in their structure depending on the observed gas emission. This study analyzes the atomic jet and molecular outflow in the Class I protostar, TMC1A to characterize morphology and identify previously undetected spatial features with JWST's NIRSpec IFU. In addition to identifying a large number of Fe II and H2 lines, we have detected the bipolar Fe jet by revealing, for the first time, the presence of a red-shifted atomic jet. Similarly, the red-shifted component of the H2 slower wide-angle outflow is observed. Both Fe II and H2 red-shifted emission exhibit significantly lower flux densities compared to their blue-shifted counterparts. Additionally, we report the detection of a collimated high-velocity (100 km s-1), blue-shifted H2 outflow, suggesting the presence of a molecular jet in addition to the well-known wider angle low-velocity structure. The Fe II and H2 jets show multiple intensity peaks along the jet axis, which may be associated with ongoing or recent outburst events. In addition to the variation in their intensities, the H2 wide-angle outflow exhibits a "ring"-like structure. The blue-shifted H2 outflow also shows a left-right brightness asymmetry likely due to interactions with the surrounding ambient medium and molecular outflows. Using the Fe II line ratios, the extinction along the atomic jet is estimated to be between Av = 10-30 on the blue-shifted side, with a trend of decreasing extinction with distance from the protostar. A similar Av is found for the red-shifted side, supporting the argument for an intrinsic red-blue outflow lobe asymmetry rather than environmental effects such as extinction. This intrinsic difference revealed by the unprecedented sensitivity of JWST, suggests that younger outflows already exhibit the red-blue side asymmetry more commonly observed towards jets associated with Class II disks., Comment: 16 pages, 11 figures

Optical trapping enables precise control of individual particles of different sizes, such as atoms, molecules, or nanospheres. Optical tweezers provide free-space omnidirectional optical trapping of objects in laboratories around the world. As an alternative to standard macroscopic setups based on lenses, which are inherently bound by the diffraction limit, plasmonic and photonic nanostructures promise trapping by near-field optical effects on the extreme nanoscale. However, the practical design of lossless waveguide-coupled nanostructures capable of trapping sub-wavelength-sized particles in all spatial directions has until now proven insurmountable. In this work, we demonstrate an omnidirectional optical trap realized by inverse-designing fabrication-ready integrated dielectric nanocavities. The sub-wavelength optical trap is designed to rely solely on the gradient force and is thus particle-size agnostic. In particular, we show how a trapped particle with a radius of 15 nm experiences a force strong enough to overcome room-temperature thermal fluctuations. Furthermore, through the robust inverse design framework, we tailor manufacturable devices operating at short-wave infrared and near-infrared wavelengths. Our results open a new regime of levitated optical trapping by achieving a deep trapping potential capable of trapping single sub-wavelength particles in all directions using optical gradient forces. We anticipate potentially groundbreaking applications of the optimized optical trapping system for biomolecular analysis in aqueous environments, levitated cavity-optomechanics, and cold atom physics, constituting an important step towards realizing integrated bio-nanophotonics and mesoscopic quantum mechanical experiments.

Physiological whole-body models are valuable tools for the development of novel drugs where understanding the system aspects is important. This paper presents a generalized model that encapsulates the structure and flow of whole-body human physiology. The model contains vascular, interstitial, and cellular subcompartments for each organ. Scaling of volumes and blood flows is described to allow for investigation across populations or specific patient groups. The model equations and the corresponding parameters are presented along with a catalog of functions that can be used to define the organ transport model and the biochemical reaction model. A simple example illustrates the procedure., Comment: 6 pages, 3 figures, 3 tables, submitted to be presented at a conference

Cardiovascular diseases are the leading cause of death. Increased levels of plasma cholesterol are consistently associated with an increased risk of cardiovascular disease. As a result, it is imperative that studies are conducted to determine the best course of action to reduce whole-body cholesterol levels. A whole-body mathematical model for cholesterol metabolism and transport is proposed. The model can simulate the effects of lipid-lowering drugs like statins and anti-PCSK9. The model is based on ordinary differential equations and kinetic functions. It has been validated against literature data. It offers a versatile platform for designing personalized interventions for cardiovascular health management., Comment: 6 pages, 10 figures, submitted to be presented at a conference

Current language models require a lot of training data to obtain high performance. For Relation Classification (RC), many datasets are domain-specific, so combining datasets to obtain better performance is non-trivial. We explore a multi-domain training setup for RC, and attempt to improve performance by encoding domain information. Our proposed models improve > 2 Macro-F1 against the baseline setup, and our analysis reveals that not all the labels benefit the same: The classes which occupy a similar space across domains (i.e., their interpretation is close across them, for example "physical") benefit the least, while domain-dependent relations (e.g., "part-of'') improve the most when encoding domain information., Comment: Accepted at LREC-COLING 2024

We study Quantum Chromodynamics in the chiral large $N_c$ limit which contains a left-handed Weyl fermion in the fundamental representation, a left-handed Weyl fermion in the two index antisymmetric representation and $(N_c-3)$ left-handed Weyl fermions in the antifundamental representation of the $SU(N_c)$ gauge group. We construct gauge singlet composite operators and study their masses and correlation functions at large $N_c$. It is shown that all hadron masses scale as $\sim N_c^0 n_q$ where $n_q$ is the number of constituent quarks in the hadron. In addition by simple gluon exchange considerations it is seen that scattering amplitudes between hadrons have the same $N_c$ scaling as the mass of the lightest hadron involved. This is the case provided the hadrons in the scattering amplitude share a sufficiently large number of constituent quarks. The chiral large $N_c$ extension also allows for other non-trivial processes. For instance we consider two different baryonium states that are unique to this extension and that decay via emissions of two- and three-quark hadrons. Also other non-trivial scattering processes are considered. Finally, we study composites made of a mix of left- and right-handed fields. We categorize multiple groups of hadrons within the full spectrum according to their flavor structure. Within these groups all $n$-point functions scale the same.

The investigation of the fluctuations in interacting quantum systems at finite temperatures showcases the ongoing challenges in understanding complex quantum systems. Recently, atom number fluctuations in weakly interacting Bose-Einstein condensates were observed, motivating an investigation of the thermal component of partially condensed Bose gases. Here, we present a combined analysis of both components, revealing the presence of fluctuations in the thermal component. This analysis includes a comprehensive statistical evaluation of uncertainties in the preparation and parameter estimation of partially condensed Bose gases. Using Monte Carlo simulations of optical density profiles, we estimate the noise contributions to the atom number and temperature estimation of the condensed and thermal cloud, which is generally applicable in the field of ultracold atoms. Furthermore, we investigate the specific noise contributions in the analysis of atom number fluctuations and show that preparation noise in the total atom number leads to an important technical noise contribution. Subtracting all known noise contributions from the variance of the atom number in the BEC and thermal component allows us to improve the estimate of the fundamental peak fluctuations.

The accurate determination of atom numbers is an ubiquitous problem in the field of ultracold atoms. For modest atom numbers, absolute calibration techniques are available, however, for large numbers and high densities, the available techniques neglect many-body scattering processes. Here, a spatial calibration technique for time-of-flight absorption images of ultracold atomic clouds is presented. The calibration is obtained from radially averaged absorption images and we provide a practical guide to the calibration process. It is shown that the calibration coefficient scales linearly with optical density and depends on the absorbed photon number for the experimental conditions explored here. This allows for the direct inclusion of a spatially dependent calibration in the image analysis. For typical ultracold atom clouds the spatial calibration technique leads to corrections in the detected atom number up to $\approx\! 12\,\%$ and temperature up to $\approx \!14\,\%$ in comparison to previous calibration techniques. The technique presented here addresses a major difficulty in absorption imaging of ultracold atomic clouds and prompts further theoretical work to understand the scattering processes in ultracold dense clouds of atoms for accurate atom number calibration.

Alkali trimers, Ak$_3$, located on the surface of He nanodroplets are triply ionized following multiphoton absorption from an intense femtosecond laser pulse leading to fragmentation into three correlated Ak$^+$ ions. Combining the information from three-fold covariance analysis of the emission direction of the fragment ions and from their kinetic energy distributions $P(E_{\text{kin}})$, we find that Na$_3$, K$_3$, and Rb$_3$ have an equilateral triangular structure, corresponding to that of the lowest-lying quartet state $^{4}\mathrm{A}_{2}'$, and determine the equilibrium bond distance $R_\text{eq}$(Na$_3$) = 4.65 $\pm$ 0.15 {\AA}, $R_\text{eq}$(K$_3$) = 5.03 $\pm$ 0.18 {\AA}, and $R_\text{eq}$(Rb$_3$) = 5.45 $\pm$ 0.22 {\AA}. For K$_3$ and Rb$_3$ these values agree well with existing theoretical calculations, while for Na$_3$ the value is 0.2-0.3 {\AA} larger than the existing theoretical results. The discrepancy is ascribed to a minor internuclear motion of Na$_3$ during the ionization process. Also, we determine the distribution of internuclear distances $P(R)$ under the assumption of fixed bond angles. The results are compared to the square of the internuclear wave function $|\Psi(R)|^2$., Comment: 7 pages, 5 figures

Difficulty is one of the key drivers of player engagement and it is often one of the aspects that designers tweak most to optimise the player experience; operationalising it is, therefore, a crucial task for game development studios. A common practice consists of creating metrics out of data collected by player interactions with the content; however, this allows for estimation only after the content is released and does not consider the characteristics of potential future players. In this article, we present a number of potential solutions for the estimation of difficulty under such conditions, and we showcase the results of a comparative study intended to understand which method and which types of data perform better in different scenarios. The results reveal that models trained on a combination of cohort statistics and simulated data produce the most accurate estimations of difficulty in all scenarios. Furthermore, among these models, artificial neural networks show the most consistent results.

We consider a strengthening of the usual quasiconvexity condition of Morrey in two dimensions, which allows us to prove lower semicontinuity for functionals which are unbounded as the determinant vanishes. This notion, that we call principal quasiconvexity, arose from the planar theory of quasiconformal mappings and mappings of finite distortion. We compare it with other quasiconvexity conditions that have appeared in the literature and provide a number of concrete examples of principally quasiconvex functionals that are not polyconvex. The Stoilow factorization, that in the context of maps of integrable distortion was developed by Iwaniec and \v{S}ver\'ak, plays a prominent role in our approach., Comment: 20 pages

Simulating chemical systems is highly sought after and computationally challenging, as the simulation cost exponentially increases with the system size. Quantum computers have been proposed as a computational means to overcome this bottleneck. Most efforts recently have been spent on determining the ground states of chemical systems. Hardness results and the lack of efficient heuristics for initial-state generation sheds doubt on the feasibility. Here we propose an inherently efficient approach for solving chemical simulation problems, meaning it requires quantum circuits of size scaling polynomially in relevant system parameters. If a set of assumptions can be satisfied, our approach finds good initial states by assembling initial states for dynamical simulation in a scattering tree. We discuss a variety of quantities of chemical interest that can be measured based on quantum simulation, e.g. of a reaction, succeeding the initial state preparation., Comment: 12 pages, 4 figures

We introduce a new quantification of nonuniform ellipticity in variational problems via convex duality, and prove higher differentiability and $2d$-smoothness results for vector valued minimizers of possibly degenerate functionals. Our framework covers convex, anisotropic polynomials as prototypical model examples - in particular, we improve in an essentially optimal fashion Marcellini's original results \cite{ma1}., Comment: 34 pages

Knowledge about statistics for water level variations along the coast due to storm surge is important for the utilization of the coastal zone. An open and freely available storm surge hindcast archive covering the coast of Norway and adjacent sea areas spanning the time period 1979-2022 is presented. The storm surge model is forced by wind stress and mean sea level pressure taken from the non-hydrostatic NORA3 atmospheric hindcast. A dataset consisting of observations of water level from more than 90 water level gauges along the coasts of the North Sea and the Norwegian Sea is compiled and quality controlled, and used to assess the performance of the hindcast. The observational dataset is distributed in both time and space, and when considering all the available quality controlled data, the comparison with modelled water levels yield a mean absolute error (MAE) of 9.7 cm and a root mean square error (RMSE) of 12.4 cm. Values for MAE and RMSE scaled by the standard deviation of the observed storm surge for each station are 0.42 and 0.54 standard deviations, repsectively. When considering the geographical differences in characteristics of storm surge for different countries/regions, the values of MAE and RMSE are in the range 5.7-13.9 cm and 7.6-17.8 cm respectively, and 0.33-0.46 and 0.42-0.59 standard deviations for the scaled values. The minimum and maximum values for water level in the hindcast are -2.60 m and 3.92 m. In addition, 100-year return level estimates are calculated from the hindcast, with minimum and maximum values of, respectively, -2.75 m and 3.98 m. All minimum and maximum values are found in the southern North Sea area.

We present a comprehensive investigation of the light-matter interaction dynamics in two-dimensional materials coupled with a spectrally isolated cavity mode in the strong coupling regime. The interaction between light and matter breaks the translational symmetry of excitons in the two-dimensional lattice and results in the emergence of a localized polariton state. Employing a novel approach involving transformation to exciton reaction coordinates, we derive a Markovian master equation to describe the formation of a macroscopic population in the localized polariton state. Our study shows that the construction of a large-scale polariton population is affected by correction terms addressing the breakdown of translational symmetry. Increasing the spatial width of the cavity mode increases the Coulomb scattering rates while the correction terms saturate and affect the system's dynamics progressively less. Tuning the lattice temperature can induce bistability and hysteresis with different origins than those recognized for quantum wells in larger microcavities. We identify a limit temperature $T_{\mathrm{l}}$ as a key factor for stimulated emissions and forming a macroscopic population, enriching our understanding of strong coupling dynamics in systems with extreme confinement., Comment: 15 pages, 15 figures

In this paper, harkening back to ideas of Hardy and Ramanujan, Mahler and de Bruijn, with the addition of more recent results on the Fibonacci Dirichlet series, we determine the asymptotic number of ways $p_F(n)$ to write an integer as the sum of non-distinct Fibonacci numbers. This appears to be the first such asymptotic result concerning non-distinct partitions over Fibonacci numbers. As well, under weak conditions, we prove analogous results for a general linear recurrences., Comment: 17 Pages. V2 does not address distinct partitions--there was a nuanced (fatal) flaw in that part of the paper

We present an optical cavity with deep sub-wavelength confinement of light in a region that simultaneously works as a quantum dot. The design is based on a dielectric membrane with a buried quantum well and restricts the electron and hole wave functions to the area of the optical hotspot in order to overcome the challenge of co-locating an optical cavity with a quantum emitter. Combined with proper surface passivation, this geometry points towards the deterministic fabrication of functional quantum dots in optical cavities by lithographic means.