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Context. White-light stellar flares are proxies for some of the most energetic types of flares, but their triggering mechanism is still poorly understood. As they are associated with strong X and UV emission, their study is particularly relevant to estimate the amount of high-energy irradiation onto the atmospheres of exoplanets, especially those in their stars' habitable zone. Aims. We used the high-cadence, high-photometric capabilities of the CHEOPS and TESS space telescopes to study the detailed morphology of white-light flares occurring in a sample of 130 late-K and M stars, and compared our findings with results obtained at a lower cadence. We developed dedicated software for this purpose. Results. Multi-peak flares represent a significant percentage ($\gtrsim 30$\%) of the detected outburst events. Our findings suggest that high-impulse flares are more frequent than suspected from lower-cadence data, so that the most impactful flux levels that hit close-in exoplanets might be more time-limited than expected. We found significant differences in the duration distributions of single-peak and complex flare components, but not in their peak luminosity. A statistical analysis of the flare parameter distributions provides marginal support for their description with a log-normal instead of a power-law function, leaving the door open to several flare formation scenarios. We tentatively confirmed previous results about quasi-periodic pulsations in high-cadence photometry, report the possible detection of a pre-flare dip, and did not find hints of photometric variability due to an undetected flare background. Conclusions. The high-cadence study of stellar hosts might be crucial to evaluate the impact of their flares on close-in exoplanets, as their impulsive phase emission might otherwise be incorrectly estimated. Future telescopes such as PLATO and Ariel will help in this respect., Comment: 28 pages, 25 figures, 4 tables, to be published in Astronomy & Astrophysics

An efficient way to study the QCD phase diagram at small finite density is to extrapolate thermodynamical observables from imaginary chemical potential. The phase diagram features a crossover line starting from the transition temperature already determined at zero chemical potential. In this work we focus on the Taylor expansion of this line up to $\mu^4$ contributions. We present the continuum extrapolation of the crossover temperature based on different observables at several lattice spacings., Comment: Proceedings to Quark Matter Conference 2019

We aim to constrain the internal structure and composition of HD 15337 b and c, two short-period planets situated on opposite sides of the radius valley, using new transit photometry and radial velocity data. We acquire 6 new transit visits with the CHaracterising ExOPlanet Satellite (CHEOPS) and 32 new radial velocity measurements from the High Accuracy Radial Velocity Planet Searcher (HARPS) to improve the accuracy of the mass and radius estimates for both planets. We reanalyse light curves from TESS sectors 3 and 4 and analyse new data from sector 30, correcting for long-term stellar activity. Subsequently, we perform a joint fit of the TESS and CHEOPS light curves, and all available RV data from HARPS and the Planet Finder Spectrograph (PFS). Our model fits the planetary signals, the stellar activity signal and the instrumental decorrelation model for the CHEOPS data simultaneously. The stellar activity was modelled using a Gaussian-process regression on both the RV and activity indicators. We finally employ a Bayesian retrieval code to determine the internal composition and structure of the planets. We derive updated and highly precise parameters for the HD 15337 system. Our improved precision on the planetary parameters makes HD 15337 b one of the most precisely characterised rocky exoplanets, with radius and mass measurements achieving a precision better than 2\% and 7\%, respectively. We are able to improve the precision of the radius measurement of HD 15337 c to 3\%. Our results imply that the composition of HD 15337 b is predominantly rocky, while HD 15337 c exhibits a gas envelope with a mass of at least $0.01\ M_\oplus$.Our results lay the groundwork for future studies, which can further unravel the atmospheric evolution of these exoplanets and give new insights into their composition and formation history and the causes behind the radius gap., Comment: 17 pages, including appendix

Context. Identifying minerals on asteroid surfaces is difficult as space weathering modifies the minerals infrared spectra. This shouldbe better understood for proper interpretation. Aims. We simulated the space weathering effects on a meteorite and recorded the alterations of the crystalline structure, such as the change in peak positions and full width at half maximum values. Methods. We used proton irradiation to simulate the effects of solar wind on a sample of NWA 10580 CO3 chondrite meteorites. After irradiation in three gradually increased steps with 1 keV ion energy, we used infrared microscopic reflectance and diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) to identify and understand the consequences of irradiation. Results. We find negative peak shifts after the first and second irradiations at pyroxene and feldspar minerals, similarly to the literature, and this shift was attributed to Mg loss. However, after the third irradiation a positive change in values in wavenumber emerged for silicates, which could come from the distortion of SiO4 tetrahedra, resembling shock deformation. The full width at half maximum values of major bands show a positive (increasing) trend after irradiations in the case of feldspars, using IR reflection measurements. Comparing DRIFTS and reflection infrared data, the peak positions of major mineral bands were at similar wavenumbers, but differences can be observed in minor bands. Conclusions. We measured the spectral changes of meteorite minerals after high doses of proton irradiation for several minerals. We show the first of these measurements for feldspars; previous works only presented pyroxene, olivine, and phyllosilicates.

Context. Gaia18cjb is one of the Gaia-alerted eruptive young star candidates which has been experiencing a slow and strong brightening during the last 13 years, similar to some FU Orionis-type objects. Aims. The aim of this work is to derive the young stellar nature of Gaia18cjb, determine its physical and accretion properties to classify its variability. Methods. We conducted monitoring observations using multi-filter optical and near-infrared photometry, as well as near-infrared spectroscopy. We present the analysis of pre-outburst and outburst optical and infrared light curves, color-magnitude diagrams in different bands, the detection of near-IR spectral lines, and estimates of both stellar and accretion parameters during the burst. Results. The optical light curve shows an unusually long (8 years) brightening event of 5 mag in the last 13 years, before reaching a plateau indicating that the burst is still on-going, suggesting a FUor-like nature. The same outburst is less strong in the infrared light curves. The near-infrared spectra, obtained during the outburst, exhibit emission lines typical of highly accreting low-intermediate mass young stars with typical EXor features. The spectral index of Gaia18cjb SED classifies it as a Class I in the pre-burst stage and a Flat Spectrum young stellar object (YSO) during the burst. Conclusions. Gaia18cjb is an eruptive YSO which shows FUor-like photometric features (in terms of brightening amplitude and length of the burst) and EXor-like spectroscopic features and accretion rate, as V350 Cep and V1647 Ori, classified as objects in between FUors and EXors, Comment: 21 pages, 13 figures

Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge 2$ random variables. Probably the most widespread independence measure relying on kernels is the so-called Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades ago, the fundamental question of the rate at which HSIC can be estimated is still open. In this work, we prove that the minimax optimal rate of HSIC estimation on $\mathbb R^d$ for Borel measures containing the Gaussians with continuous bounded translation-invariant characteristic kernels is $\mathcal O\!\left(n^{-1/2}\right)$. Specifically, our result implies the optimality in the minimax sense of many of the most-frequently used estimators (including the U-statistic, the V-statistic, and the Nystr\"om-based one) on $\mathbb R^d$., Comment: Accepted for publication at NeurIPS 2024

We undertake a detailed study of the gaugings of two-dimensional Yang-Mills theory by its intrinsic charge conjugation 0-form and centre 1-form global symmetries, elucidating their higher algebraic and geometric structures, as well as the meaning of dual lower form symmetries. Our derivations of orbifold gauge theories make use of a combination of standard continuum path integral methods, networks of topological defects, and techniques from higher gauge theory. We provide a unified description of higher and lower form gauge fields for a $p$-form symmetry in the geometric setting of $p$-gerbes, and derive reverse orbifolds by the dual $(-1)$-form symmetries. We identify those orbifolds in which charge conjugation symmetry is spontaneously broken, and relate the breaking to mixed anomalies involving $(-1)$-form symmetries. We extend these considerations to gaugings by the non-invertible 1-form symmetries of two-dimensional Yang-Mills theory by introducing a notion of generalized $\theta$-angle., Comment: 55 pages, 3 figures, 1 table; v2: minor changes and additions, references added

Microservice architectures have gained prominence in both academia and industry, offering enhanced agility, reusability, and scalability. To simplify scaling operations in microservice architectures, container orchestration platforms such as Kubernetes feature Horizontal Pod Auto-scalers (HPAs) designed to adjust the resources of microservices to accommodate fluctuating workloads. However, existing HPAs are not suitable for resource-constrained environments, as they make scaling decisions based on the individual resource capacities of microservices, leading to service unavailability and performance degradation. Furthermore, HPA architectures exhibit several issues, including inefficient data processing and a lack of coordinated scaling operations. To address these concerns, we propose Smart HPA, a flexible resource-efficient horizontal pod auto-scaler. It features a hierarchical architecture that integrates both centralized and decentralized architectural styles to leverage their respective strengths while addressing their limitations. We introduce resource-efficient heuristics that empower Smart HPA to exchange resources among microservices, facilitating effective auto-scaling of microservices in resource-constrained environments. Our experimental results show that Smart HPA outperforms the Kubernetes baseline HPA by reducing resource overutilization, overprovisioning, and underprovisioning while increasing resource allocation to microservice applications.

In this paper, we provide lower bounds for Differentially Private (DP) Online Learning algorithms. Our result shows that, for a broad class of $(\varepsilon,\delta)$-DP online algorithms, for number of rounds $T$ such that $\log T\leq O(1 / \delta)$, the expected number of mistakes incurred by the algorithm grows as $\Omega(\log \frac{T}{\delta})$. This matches the upper bound obtained by Golowich and Livni (2021) and is in contrast to non-private online learning where the number of mistakes is independent of $T$. To the best of our knowledge, our work is the first result towards settling lower bounds for DP-Online learning and partially addresses the open question in Sanyal and Ramponi (2022)., Comment: Accepted at the Conference on Learning Theory (COLT) 2024, Edmonton, Canada

Define an optimizer as having memory $k$ if it stores $k$ dynamically changing vectors in the parameter space. Classical SGD has memory $0$, momentum SGD optimizer has $1$ and Adam optimizer has $2$. We address the following questions: How can optimizers make use of more memory units? What information should be stored in them? How to use them for the learning steps? As an approach to the last question, we introduce a general method called "Retrospective Learning Law Correction" or shortly RLLC. This method is designed to calculate a dynamically varying linear combination (called learning law) of memory units, which themselves may evolve arbitrarily. We demonstrate RLLC on optimizers whose memory units have linear update rules and small memory ($\leq 4$ memory units). Our experiments show that in a variety of standard problems, these optimizers outperform the above mentioned three classical optimizers. We conclude that RLLC is a promising framework for boosting the performance of known optimizers by adding more memory units and by making them more adaptive.

The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often leading to unequal representation and skewed electoral outcomes. One of the few ways to detect gerrymandering is by algorithmically sampling redistricting plans. Previous methods mainly focus on sampling from some neighborhood of ``realistic' districting plans, rather than a uniform sample of the entire space. We present a deterministic subexponential time algorithm to uniformly sample from the space of all possible $ k $-partitions of a bounded degree planar graph, and with this construct a sample of the entire space of redistricting plans. We also give a way to restrict this sample space to plans that match certain compactness and population constraints at the cost of added complexity. The algorithm runs in $ 2^{O(\sqrt{n}\log n)} $ time, although we only give a heuristic implementation. Our method generalizes an algorithm to count self-avoiding walks on a square to count paths that split general planar graphs into $ k $ regions, and uses this to sample from the space of all $ k $-partitions of a planar graph., Comment: 17 Pages

Ultra-hot Jupiters present a unique opportunity to understand the physics and chemistry of planets at extreme conditions. WASP-12b stands out as an archetype of this class of exoplanets. We performed comprehensive analyses of the transits, occultations, and phase curves of WASP-12b by combining new CHEOPS observations with previous TESS and Spitzer data to measure the planet's tidal deformation, atmospheric properties, and orbital decay rate. The planet was modeled as a triaxial ellipsoid parameterized by the second-order fluid Love number, $h_2$, which quantifies its radial deformation and provides insight into the interior structure. We measured the tidal deformation of WASP-12b and estimated a Love number of $h_2=1.55_{-0.49}^{+0.45}$ (at 3.2$\sigma$) from its phase curve. We measured occultation depths of $333\pm24$ppm and $493\pm29$ppm in the CHEOPS and TESS bands, respectively, while the dayside emission spectrum indicates that CHEOPS and TESS probe similar pressure levels in the atmosphere at a temperature of 2900K. We also estimated low geometric albedos of $0.086\pm0.017$ and $0.01\pm0.023$ in the CHEOPS and TESS passbands, respectively, suggesting the absence of reflective clouds in the dayside of the WASP-12b. The CHEOPS occultations do not show strong evidence for variability in the dayside atmosphere of the planet. Finally, we refine the orbital decay rate by 12% to a value of -30.23$\pm$0.82 ms/yr. WASP-12b becomes the second exoplanet, after WASP-103b, for which the Love number has been measured (at 3$sigma$) from the effect of tidal deformation in the light curve. However, constraining the core mass fraction of the planet requires measuring $h_2$ with a higher precision. This can be achieved with high signal-to-noise observations with JWST since the phase curve amplitude, and consequently the induced tidal deformation effect, is higher in the infrared., Comment: accepted for publication in A&A

The results of a Fourier analysis of high-precision Kepler photometry of 75 double-mode RR~Lyrae (RRd) stars observed during NASA's K2 Mission (2014-18) are presented. Seventy-two of the stars are `classical' RRd (cRRd) stars lying along a well-defined curve in the Petersen diagram and showing no evidence of Blazhko modulations. The remaining three stars are `anomalous' RRd (aRRd) stars that lie well below the cRRd curve in the Petersen diagram. These stars have larger fundamental-mode amplitudes than first-overtone amplitudes and exhibit Blazhko variations. Period-amplitude relations for the individual pulsation components of the cRRd stars are examined, as well as correlations involving Fourier phase-difference and amplitude-ratio parameters that characterize the light curves for the two radial modes. A simple statistical model relating the fundamental (P0) and first-overtone (P1) periods to [Fe/H] provides insight into the functional form of the Petersen diagram. A calibration equation for estimating [Fe/H]phot abundances of `classical' RRd stars is derived by inverting the model and using 211 field and 57 globular cluster cRRd stars with spectroscopic metallicities to estimate the model coefficients. The equation is used to obtain [Fe/H]phot for the full sample of 72 K2 cRRd stars and for 2130 cRRd stars observed by the ESA Gaia Mission. Of the 49 K2 cRRd stars that are in the Gaia DR3 catalogue only five were found to be correctly classified, the remainder having been misclassified `RRc' or `RRab'., Comment: 23 pages, 12 figures, 10 tables plus Supplementary Information (two Appendices, two tables, 1 animated gif); accepted for publication in MNRAS

The diameter of a directed graph is a fundamental parameter defined as the maximum distance realized among the pairs of vertices. As graphs of small diameter are of interest in many applications, we study the following problem: for a given directed graph and a positive integer $d$, what is the minimum number of arc flips (also known as arc reversal) required to obtain a graph with diameter at most $d$? It is a generalization of the well-known problem \textsc{Oriented Diameter}, first studied by Chv\'atal and Thomassen. Here we investigate variants of the above problem, considering the number of flips and the target diameter as parameters. We prove that most of the related questions of this type are hard. Special cases of graphs are also considered, as planar and cactus graphs, where we give polynomial time algorithms., Comment: 14 pages, 3 figures

We discuss how Moyal deformations of gauge theories, which arise naturally from open string theory, fit into the paradigm of colour-kinematics duality and the double copy of gauge theory to gravity. Along the way we encounter novel noncommutative scalar field theories with rigid colour symmetry that have no interacting commutative counterparts. These scalar theories offer new perspectives on old ideas that rank one noncommutative gauge theories are gravitational theories. This is rendered explicit in four dimensions where they and their double copy images yield deformations of integrable theories describing the self-dual sectors of Yang-Mills theory and gravity., Comment: 12 pages; Contribution to the proceedings volume for "Gravity, Strings and Fields: A conference in honour of Gordon Semenoff"

We present the discovery and characterization of two warm mini-Neptunes transiting the K3V star TOI-815 in a K-M binary system. Analysis of the spectra and rotation period reveal it to be a young star with an age of $200^{+400}_{-200}$Myr. TOI-815b has a 11.2-day period and a radius of 2.94$\pm$0.05$\it{R_{\rm\mathrm{\oplus}}}$ with transits observed by TESS, CHEOPS, ASTEP, and LCOGT. The outer planet, TOI-815c, has a radius of 2.62$\pm$0.10$\it{R_{\rm\mathrm{\oplus}}}$, based on observations of three non-consecutive transits with TESS, while targeted CHEOPS photometry and radial velocity follow-up with ESPRESSO were required to confirm the 35-day period. ESPRESSO confirmed the planetary nature of both planets and measured masses of 7.6$\pm$1.5 $\it{M_{\rm \mathrm{\oplus}}}$ ($\rho_\mathrm{P}$=1.64$^{+0.33}_{-0.31}$gcm$^{-3}$) and 23.5$\pm$2.4$\it{M_{\rm\mathrm{\oplus}}}$ ($\rho_\mathrm{P}$=7.2$^{+1.1}_{-1.0}$gcm$^{-3}$) respectively. Thus, the planets have very different masses, unlike the usual similarity of masses in compact multi-planet systems. Moreover, our statistical analysis of mini-Neptunes orbiting FGK stars suggests that weakly irradiated planets tend to have higher bulk densities compared to those suffering strong irradiation. This could be ascribed to their cooler atmospheres, which are more compressed and denser. Internal structure modeling of TOI-815b suggests it likely has a H-He atmosphere constituting a few percent of the total planet mass, or higher if the planet is assumed to have no water. In contrast, the measured mass and radius of TOI-815c can be explained without invoking any atmosphere, challenging planetary formation theories. Finally, we infer from our measurements that the star is viewed close to pole-on, which implies a spin-orbit misalignment at the 3$\sigma$ level., Comment: 24 pages, 27 figures, 6 tables

Consider the Erd\H{o}s-R\'enyi random graph process $\{G_m\}_{m \ge 0}$ in which we start with an empty graph $G_0$ on the vertex set $[n]$, and in each step form $G_i$ from $G_{i-1}$ by adding one new edge chosen uniformly at random. Resolving a conjecture by Benjamini and Tzalik, we give a simple proof that w.h.p. as soon as $G_m$ has minimum degree $2$ it is globally rigid in the following sense: For any function $d \colon E(G_m) \rightarrow \mathbb{R}$, there exists at most one injective function $f \colon [n] \rightarrow \mathbb{R}$ (up to isometry) such that $d(ij) = |f(i) - f(j)|$ for every $ij \in E(G_m)$. We also resolve a related question of Gir\~{a}o, Illingworth, Michel, Powierski, and Scott in the sparse regime for the random graph and give some open problems., Comment: 5 pages

We show that the graph property of having a (very) large $k$-th Betti number $\beta_k$ for constant $k$ is testable with a constant number of queries in the dense graph model. More specifically, we consider a clique complex defined by an underlying graph and prove that for any $\varepsilon>0$, there exists $\delta(\varepsilon,k)>0$ such that testing whether $\beta_k \geq (1-\delta) d_k$ for $\delta \leq \delta(\varepsilon,k)$ reduces to tolerantly testing $(k+2)$-clique-freeness, which is known to be testable. This complements a result by Elek (2010) showing that Betti numbers are testable in the bounded-degree model. Our result combines the Euler characteristic, matroid theory and the graph removal lemma., Comment: 10 pages, 0 figures

Richmond and Richmond (American Mathematical Monthly 104 (1997), 713--719) proved the following theorem: If, in a metric space with at least five points, all triangles are degenerate, then the space is isometric to a subset of the real line. We prove that the hypothesis is unnecessarily strong: In a metric space on $n$ points, fewer than $7n^2/6$ suitably placed degenerate triangles suffice. However, fewer than $n(n-1)/2$ degenerate triangles, no matter how cleverly placed, never suffice., Comment: Supersedes arXiv:2209.14361 [math.MG]

We introduce a relativized version of random Kripke's schema and show how it may be applied in the investigation of the expressive power of intuitionistic real algebra by interpreting second-order Heyting arithmetic in it., Comment: 7 pages

We discuss properties of Quantum Chromodynamics at finite temperature obtained by means of lattice simulations with overlap fermions. This fermion discretization preserves chiral symmetry even at finite lattice spacing. We present details of the lattice formulation, first results for the chiral observables and discuss the behaviour of the system near the chiral thermal phase transition., Comment: 8 pages, 12 figures, proceedings of the Lattice 2023

In this study we employ staggered fermions to calculate the two-pion taste singlet states at rest. Leveraging the Clebsch-Gordan coefficients of the symmetry group associated with staggered fermions, we effectively compute the $\pi\pi$ contributions to the resting $\rho$-meson correlator. To discern the distinct energy states involved, we adopt a generalized eigenvalue problem-solving approach. This work will provide insight into the important role played by the two-pion contribution to the anomalous magnetic moment of the muon. In this paper we present our group theoretic considerations and preliminary results on the contribution of two-pion states to the rho meson correlation function., Comment: 8 pages, 2 tables, 5 figures

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that this approximate posterior retains the rate of recovery of the full data posterior distribution, where the rate of recovery adapts to the smoothness of the true regression function. As particular examples we consider Gaussian process priors based on integrated Brownian motion and the Mat\'ern kernel augmented with a prior on the length scale. Besides theoretical guarantees we present a numerical study of the methods both on synthetic and real world data. We also propose a new aggregation technique, which numerically outperforms previous approaches., Comment: 20 pages, 4 figures

Observations of low-mass stars have frequently shown a disagreement between observed stellar radii and radii predicted by theoretical stellar structure models. This ``radius inflation'' problem could have an impact on both stellar and exoplanetary science. We present the final results of our observation programme with the CHEOPS satellite to obtain high-precision light curves of eclipsing binaries with low mass stellar companions (EBLMs). Combined with the spectroscopic orbits of the solar-type companion, we can derive the masses, radii and effective temperatures of 23 M-dwarf stars. We use the PYCHEOPS data analysis software to analyse their primary and secondary occultations. For all but one target, we also perform analyses with TESS light curves for comparison. We have assessed the impact of starspot-induced variation on our derived parameters and account for this in our radius and effective temperature uncertainties using simulated light curves. We observe trends for inflation with both metallicity and orbital separation. We also observe a strong trend in the difference between theoretical and observational effective temperatures with metallicity. There is no such trend with orbital separation. These results are not consistent with the idea that observed inflation in stellar radius combines with lower effective temperature to preserve the luminosity predicted by low-mass stellar models. Our EBLM systems are high-quality and homogeneous measurements that can be used in further studies into radius inflation., Comment: 21 pages, 10 figures, accepted for publication in MNRAS, Supplementary material provided as ancillary files

While there is universal agreement that agents ought to act ethically, there is no agreement as to what constitutes ethical behaviour. To address this problem, recent philosophical approaches to `moral uncertainty' propose aggregation of multiple ethical theories to guide agent behaviour. However, one of the foundational proposals for aggregation - Maximising Expected Choiceworthiness (MEC) - has been criticised as being vulnerable to fanaticism; the problem of an ethical theory dominating agent behaviour despite low credence (confidence) in said theory. Fanaticism thus undermines the `democratic' motivation for accommodating multiple ethical perspectives. The problem of fanaticism has not yet been mathematically defined. Representing moral uncertainty as an instance of social welfare aggregation, this paper contributes to the field of moral uncertainty by 1) formalising the problem of fanaticism as a property of social welfare functionals and 2) providing non-fanatical alternatives to MEC, i.e. Highest k-trimmed Mean and Highest Median.

Fluctuations play a key role in the study of QCD phases. Lattice QCD is a valuable tool to calculate them, but going to high orders is challenging. Up to the fourth order, continuum results are available since 2015. We present the first continuum results for sixth order baryon fluctuations for temperatures between $T=130 - 200$ MeV, and eighth order at $T=145$ MeV in a fixed volume. We show that for $T \leq 145$ MeV, relevant for criticality search, finite volume effects are under control. Our results are in sharp contrast with well known results in the literature obtained at finite lattice spacing., Comment: 5 pages, 2 figures (main text) + 5 pages, 7 figures (supplemental material)

In this paper, we study the algebraic structure of $(\sigma,\delta)$-polycyclic codes, defined as submodules in the quotient module $S/Sf$, where $S=R[x,\sigma,\delta]$ is the Ore extension ring, $f\in S$, and $R$ is a finite but not necessarily commutative ring. We establish that the Euclidean duals of $(\sigma,\delta)$-polycyclic codes are $(\sigma,\delta)$-sequential codes. By using $(\sigma,\delta)$-Pseudo Linear Transformation, we define the annihilator dual of $(\sigma,\delta)$-polycyclic codes. Then, we demonstrate that the annihilator duals of $(\sigma,\delta)$-polycyclic codes maintain their $(\sigma,\delta)$-polycyclic nature. Furthermore, we classify when two $(\sigma,\delta)$-polycyclic codes are Hamming isometrical equivalent. By employing Wedderburn polynomials, we introduce simple-root $(\sigma,\delta)$-polycyclic codes. Subsequently, we define the $(\sigma, \delta)$-Mattson-Solomon transform for this class of codes and we address the problem of decomposing these codes by using the properties of Wedderburn polynomials., Comment: 20 pages, no figure