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High-quality (Q)-factor optical resonators with extreme temporal coherence are of both technological and fundamental importance in optical metrology, continuous-wave lasing, and semiconductor quantum optics. Despite extensive efforts in designing high-Q resonators across different spectral regimes, the experimental realization of very large Q-factors at visible wavelengths remains challenging due to the small feature size that is sensitive to fabrication imperfections, and thus is typically implemented in integrated photonics. In the pursuit of free-space optics with the benefits of large space-bandwidth product and massive parallel operations, here we design and fabricate a visible-wavelength etch-free metasurface with minimized fabrication defects and experimentally demonstrate a million-scale ultrahigh-Q resonance. A new laser-scanning momentum-space-resolved spectroscopy technique with extremely high spectral and angular resolution is developed to characterize the record-high Q-factor as well as the dispersion of the million-Q resonance in free space. By integrating monolayer WSe2 into our ultrahigh-Q meta-resonator, we further demonstrate laser-like highly unidirectional and narrow-linewidth exciton emission, albeit without any operating power density threshold. Under continuous-wave laser pumping, we observe pump-power-dependent linewidth narrowing at room temperature, indicating the potential of our meta-optics platform in controlling coherent quantum light-sources. Our result also holds great promise for applications like optical sensing, spectral filtering, and few-photon nonlinear optics.

We present a novel hybrid incompressible flow/material point method solver for simulating the combustion of flammable solids. Our approach utilizes a sparse grid representation of solid materials in the material point method portion of the solver and a hybrid Eulerian/FLIP solver for the incompressible portion. We utilize these components to simulate the motion of heated air and particulate matter as they interact with flammable solids, causing combustion-related damage. We include a novel particle sampling strategy to increase Eulerian flow accuracy near regions of high temperature. We also support control of the flame front propagation speed and the rate of solid combustion in an artistically directable manner. Solid combustion is modeled with temperature-dependent elastoplastic constitutive modeling. We demonstrate the efficacy of our method on various real-world three-dimensional problems, including a burning match, incense sticks, and a wood log in a fireplace.

We investigate the gravitational lensing by Bardeen black hole in cloud of strings (CoS) in strong field limit. The effect of CoS parameter $b$ has been outlined in comparison with Bardeen black hole lens. The impact parameter increases as we increase the CoS parameter consequently more photons approach towards lens. We also obtain magnification of relativistic images and determine relativistic Einstein rings by using the parameters of two astrophysical black hole lenses $SgrA^{*}$ and $M87^{*}$. We constrain CoS parameter of black hole using EHT observations for these black holes. We also consider the time delay of signals in the presence of CoS parameter. It is significantly measurable for supermassive black hole $M87^{*}$ than $SgrA^{*}$. This analysis would constrain the Bardeen black hole in CoS as one of the candidates of primordial gravitational lens., Comment: 20 pages

Given a totally real number field $F$, we show that there are only finitely many totally real extensions of $K$ of a fixed degree that admit a universal quadratic form defined over $F$. We further obtain several explicit classification results in the case of relative quadratic extensions., Comment: 17 pages

In order to develop robots that can effectively serve as versatile and capable home assistants, it is crucial for them to reliably perceive and interact with a wide variety of objects across diverse environments. To this end, we proposed Open Vocabulary Mobile Manipulation as a key benchmark task for robotics: finding any object in a novel environment and placing it on any receptacle surface within that environment. We organized a NeurIPS 2023 competition featuring both simulation and real-world components to evaluate solutions to this task. Our baselines on the most challenging version of this task, using real perception in simulation, achieved only an 0.8% success rate; by the end of the competition, the best participants achieved an 10.8\% success rate, a 13x improvement. We observed that the most successful teams employed a variety of methods, yet two common threads emerged among the best solutions: enhancing error detection and recovery, and improving the integration of perception with decision-making processes. In this paper, we detail the results and methodologies used, both in simulation and real-world settings. We discuss the lessons learned and their implications for future research. Additionally, we compare performance in real and simulated environments, emphasizing the necessity for robust generalization to novel settings.

We study the universality of forms of degree greater than 2 over rings of integers of totally real number fields. We show that such universal forms always exist, but cannot be characterized by any variant of the 290-Theorem of Bhargava-Hanke., Comment: 11 pages

We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove that this phenomenon happens infinitely often, and, conversely, establish finiteness results about the situation when the quadratic form is fixed., Comment: preprint, 10 pages

For an algebraic number $\alpha$, let $h(\alpha)$ denote its logarithmic Weil height. In 2002, Bombieri and Zannier obtained lower bounds for Weil height for totally $p$-adic extensions of $\mathbb{Q}$, i.e., infinite Galois extension over $\mathbb{Q}$ with finite local degree over a rational prime $p$. In this paper, we formulate and prove the non-Galois analogue of this result. In particular, it leads to a $p$-adic equidistribution result i.e., if a positive proportion of conjugates of $\alpha\in\overline{\mathbb{Q}}$ lie in a finite local extension $K_{v}/\mathbb{Q}_p$, then we obtain absolute lower bound for $h(\alpha)$. We also undertake the analoguous problem for canonical height of an elliptic curve $E/K$ and obtain explicit lower bounds for them on certain non-Galois infinite extensions., Comment: 26 pages. Comments are welcome

Measurement-induced quantum computation with continuous-variable cluster states utilizes teleportation propagating the states through the cluster accompanied by non-Gaussian measurements and feedforward control. We analyze such propagation of a quantum non-Gaussian state with nonlinear squeezing through a small cluster state and show that when a nonlinear feedforward is involved in the teleportation protocol, higher nonlinear squeezing can be transferred. In a probabilistic regime, the improvement can be manifested even with current experimental resources. Better processing of non-Gaussian states can bring us closer to the necessary interplay between cluster states and non-Gaussianity required by quantum computing., Comment: references added

We establish a new connection between sails, a key notion in the geometric theory of generalised continued fractions, and arithmetic of totally real number fields, specifically, universal quadratic forms and additively indecomposable integers. Our main application is to biquadratic fields, for which we show that if their signature rank is at least 3, then ranks of universal forms and numbers of indecomposables grow as a power of the discriminant. We also construct a family in which these numbers grow only logarithmically., Comment: 21 pages

We classify all totally real number fields of degree at most 5 that admit a universal quadratic form with rational integer coefficients; in fact, there are none over the previously unsolved cases of quartic and quintic fields. This fully settles the lifting problem for universal forms in degrees at most 5. The main tool behind the proof is a computationally intense classification of fields in which every multiple of 2 is the sum of squares. We further extend these results to some real cyclotomic fields of large degrees and prove Kitaoka's conjecture for them., Comment: 19 pages

This paper focuses on the feedback global stabilization and observer construction for a sterile insect technique model. The Sterile Insect Technique (SIT) is one of the most ecological methods for controlling insect pests responsible for worldwide crop destruction and disease transmission. In this work, we construct a feedback law that globally asymptotically stabilizes a SIT model at extinction equilibrium. Since the application of this type of control requires the measurement of different states of the target insect population, and in practice, some states are more difficult and very expensive to measure than others, it is important to know how to construct a state estimator which from a few measured states, estimates the other ones as the one we build in the second part of our work. In the last part of our work, we show that we can apply the feedback control with estimated states to stabilize the full system.

Let $\zeta_K(s)$ denote the Dedekind zeta-function associated to a number field $K$. In this paper, we give an effective upper bound for the height of first non-trivial zero other than $1/2$ of $\zeta_K(s)$ under the generalized Riemann hypothesis. This is a refinement of the earlier bound obtained by Omar Sami.

Recent proposals are emerging for the experimental detection of entanglement mediated by classical gravity, carrying significant theoretical and observational implications. In fact, the detection of gravitational waves (GWs) in LIGO provides an alternative laboratory for testing various gravity-related properties. By employing LIGO's arms as oscillators interacting with gravitational waves (GWs), our study demonstrates the potential for generating quantum entanglement between two mutually orthogonal modes of simple harmonic oscillators. Our findings reveal unique entanglement dynamics, including periodic "collapse and revival" influenced by GW oscillations, alongside a distinct "quantum memory effect." Effectively, each harmonic oscillator feels a temperature. We believe that these forecasts may hold significance towards both theoretically probing and experimentally verifying various properties of classical gravitational waves., Comment: Modified version, new results added, to appear in Phys. Lett. B

This report introduces our UniTeam agent - an improved baseline for the "HomeRobot: Open Vocabulary Mobile Manipulation" challenge. The challenge poses problems of navigation in unfamiliar environments, manipulation of novel objects, and recognition of open-vocabulary object classes. This challenge aims to facilitate cross-cutting research in embodied AI using recent advances in machine learning, computer vision, natural language, and robotics. In this work, we conducted an exhaustive evaluation of the provided baseline agent; identified deficiencies in perception, navigation, and manipulation skills; and improved the baseline agent's performance. Notably, enhancements were made in perception - minimizing misclassifications; navigation - preventing infinite loop commitments; picking - addressing failures due to changing object visibility; and placing - ensuring accurate positioning for successful object placement.

We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadratic forms over a given number field $K$, under the assumption that the codifferent of $K$ is generated by a totally positive element. Motivated by a possible path to remove that assumption, we also investigate the smallest number of generators for the positive part of ideals in totally real numbers fields., Comment: 12 pages. Preprint

One of the central questions in control theory is achieving stability through feedback control. This paper introduces a novel approach that combines Reinforcement Learning (RL) with mathematical analysis to address this challenge, with a specific focus on the Sterile Insect Technique (SIT) system. The objective is to find a feedback control that stabilizes the mosquito population model. Despite the mathematical complexities and the absence of known solutions for this specific problem, our RL approach identifies a candidate solution for an explicit stabilizing control. This study underscores the synergy between AI and mathematics, opening new avenues for tackling intricate mathematical problems., Comment: 16 pages, 5 figures

We present multi-wavelength temporal and spectral characteristics of a magnetic cataclysmic variable (MCV) Swift J0503.7-2819, using far ultraviolet (FUV) and X-ray data from AstroSat, supplemented with optical data from the Southern African Large Telescope and X-ray data from the XMM-Newton and Swift observatories. The X-ray modulations at 4897.6657 s and 3932.0355 s are interpreted as the orbital ($P_{\Omega}$) and spin ($P_{\omega}$) period, respectively, and are consistent with prior reports. With a spin-orbit period ratio of 0.8 and $P_{\Omega}$ falling below the period gap (2-3 hrs) of CVs, Swift J0503.7-2819 would be the newest addition to the growing population of nearly synchronous MCVs, which we call EX Hya-like systems. Hard X-ray luminosity of $<$ $2.5\times10^{32} erg s^{-1}$, as measured with the Swift Burst Alert Telescope, identifies it to be a low-luminosity intermediate polar, similar to other EX Hya-like systems. The phenomenology of the light curves and the spectral characteristics rule out a purely disc-fed/stream-fed model and instead reveal the presence of complex accretion structures around the white dwarf. We propose a ring-like accretion flow, akin to EX Hya, using period ratio, stability arguments, and observational features. An attempt is made to differentiate between the asynchronous polar/nearly-synchronous intermediate polar nature of Swift J0503.7-2819. Further, we note that with the advent of sensitive surveys, a growing population of MCVs that exhibit characteristics of both polars and intermediate polars is beginning to be identified, likely forming a genealogical link between the two conventional classes of MCVs., Comment: Accepted for publication in MNRAS, 17 Pages, 13 Figures

Schr\"odinger cat states, which are superpositions of macroscopically distinct states, are potentially critical resources for upcoming quantum information technologies. In this paper, we introduce a scheme to generate entangled Schr\"odinger cat states in a non-relativistic electric dipole system situated on a two-dimensional plane, along with an external potential and a uniform strong magnetic field perpendicular to the plane. Additionally, our findings demonstrate that this setup can lead to the phenomenon of collapse and revival of entanglement for a specific range of our model parameters, Comment: Revised version with new figures added, to be published in Physical Review A

In this paper, we establish lower bounds on Weil height of algebraic integers in terms of the low lying zeros of the Dedekind zeta-function. As a result, we prove Lehmer's conjecture for certain infinite non-Galois extensions conditional on GRH. We also introduce and study a condition on prime ideals with small norms for arbitrary infinite extensions, in the spirit of a prime splitting condition for infinite Galois extensions introduced by E. Bombieri and U. Zannier.

We show that if a universal quadratic form exists over an infinite degree, totally real extension of the field of rationals $\mathbb{Q}$, then the set of totally positive integers in the extension does not have the Northcott property. In particular, this implies that no universal form exists over the compositum of all totally real Galois fields of a fixed prime degree over $\mathbb{Q}$. Further, by considering the existence of infinitely many square classes of totally positive units, we show that no classical universal form exists over the compositum of all such fields of degree $3d$ (for each fixed odd integer $d$)., Comment: preprint, 18 pages. Update with slight extension of Theorem 3.1, several references and small remarks added

In the Mathur-Mukhi-Sen (MMS) classification scheme for rational conformal field theories (RCFTs), a RCFT is identified by a pair of non-negative integers $\mathbf{[n, \ell]}$, with $\mathbf{n}$ being the number of characters and $\mathbf{\ell}$ the Wronskian index. The modular linear differential equation (MLDE) that the characters of a RCFT solve are labelled similarly. All RCFTs with a given $\mathbf{[n, \ell]}$ solve the modular linear differential equation (MLDE) labelled by the same $\mathbf{[n, \ell]}$. With the goal of classifying $\mathbf{[3,3]}$ and $\mathbf{[3,4]}$ CFTs, we set-up and solve those MLDEs, each of which is a three-parameter non-rigid MLDE, for character-like solutions. In the former case, we obtain four infinite families and a discrete set of $15$ solutions, all in the range $0 < c \leq 32$. Amongst these $\mathbf{[3,3]}$ character-like solutions, we find pairs of them that form coset-bilinear relations with meromorphic CFTs/characters of central charges $16, 24, 32, 40, 48, 56, 64$. There are six families of coset-bilinear relations where both the RCFTs of the pair are drawn from the infinite families of solutions. There are an additional $23$ coset-bilinear relations between character-like solutions of the discrete set. The coset-bilinear relations should help in identifying the $\mathbf{[3,3]}$ CFTs. In the $\mathbf{[3,4]}$ case, we obtain nine character-like solutions each of which is a $\mathbf{[2,2]}$ character-like solution adjoined with a constant character., Comment: 64 pages, 20 tables

Heatwaves and bushfires cause substantial impacts on society and ecosystems across the globe. Accurate information of heat extremes is needed to support the development of actionable mitigation and adaptation strategies. Regional climate models are commonly used to better understand the dynamics of these events. These models have very large input parameter sets, and the parameters within the physics schemes substantially influence the model's performance. However, parameter sensitivity analysis (SA) of regional models for heat extremes is largely unexplored. Here, we focus on the southeast Australian region, one of the global hotspots of heat extremes. In southeast Australia Weather Research and Forecasting (WRF) model is the widely used regional model to simulate extreme weather events across the region. Hence in this study, we focus on the sensitivity of WRF model parameters to surface meteorological variables such as temperature, relative humidity, and wind speed during two extreme heat events over southeast Australia. Due to the presence of multiple parameters and their complex relationship with output variables, a machine learning (ML) surrogate-based global sensitivity analysis method is considered for the SA. The ML surrogate-based Sobol SA is used to identify the sensitivity of 24 adjustable parameters in seven different physics schemes of the WRF model. Results show that out of these 24, only three parameters, namely the scattering tuning parameter, multiplier of saturated soil water content, and profile shape exponent in the momentum diffusivity coefficient, are important for the considered meteorological variables. These SA results are consistent for the two different extreme heat events. Further, we investigated the physical significance of sensitive parameters. This study's results will help in further optimising WRF parameters to improve model simulation.

We study ideal-simple commutative semirings and summarize the results giving their classification, in particular when they are finitely generated. In the principal case of (para)semifields, we then consider their minimal number of generators and show that it grows linearly with the depth of an associated rooted forest., Comment: 12 pages

We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it to prove that a number of vectors has an eventually periodic expansion in the Algebraic Jacobi--Perron Algorithm. Further, we give criteria for vectors to have purely periodic expansions; in particular, the vector cannot be totally positive., Comment: 31 pages

The Sterile Insect Technique or SIT is presently one of the most ecological methods for controlling insect pests responsible for disease transmission or crop destruction worldwide. This technique consists of releasing sterile males into the insect pest population. This approach aims at reducing fertility in the population and, consequently, reduce significantly the native insect population after a few generations. In this work, we study the global stabilization of a pest population at extinction equilibrium by the SIT method. We construct explicit feedback laws that stabilize the model and do numerical simulations to show the efficiency of our feedback laws. The different feedback laws are also compared taking into account their possible implementation in field interventions.

We study partitions of complex numbers as sums of non-negative powers of a fixed algebraic number $\beta$. We prove that if $\beta$ is real quadratic, then the number of partitions is always finite if and only if some conjugate of $\beta$ is larger than 1. Further, we show that for $\beta$ satisfying a certain condition, the partition function attains all non-negative integers as values., Comment: 10 pages, to appear in Ramanujan J

It is well known that the full matrix ring over a skew-field is a simple ring. We generalize this theorem to the case of semirings. We characterize the case when the matrix semiring $\mathbf{M}_n(S)$, of all $n\times n$ matrices over a semiring $S$, is congruence-simple, provided that either $S$ has a multiplicatively absorbing element or $S$ is commutative and additively cancellative., Comment: 11 pages

We study a new connection between multidimensional continued fractions, such as Jacobi--Perron algorithm, and additively indecomposable integers in totally real cubic number fields. First, we find the indecomposables of all signatures in Ennola's family of cubic fields, and use them to determine the Pythagoras numbers. Second, we compute a number of periodic JPA expansions, also in Shanks' family of simplest cubic fields. Finally, we compare these expansions with indecomposables to formulate our conclusions.

We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More generally, we obtain such a result for totally positive definite quadratic lattices that represent all the multiples of a given rational integer. Our main tools are short vectors in quadratic lattices combined with an estimate for the number of periodic continued fractions with bounded coefficients., Comment: 18 pages, minor changes

We give an overview of universal quadratic forms and lattices, focusing on the recent developments over the rings of integers in totally real number fields. In particular, we discuss indecomposable algebraic integers as one of the main tools., Comment: 34 pages, journal version