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Consider f : Ωn K →C a function from the n-fold product of multiplicative cyclic groups of order K. Any such f may be extended via its Fourier expansion to an analytic polynomial on the polytorus Tn, and the set of such polynomials coincides with the set of all analytic polynomials on Tn of individual degree at most K−1. In this setting it is natural to ask how the supremum norms of f over Tn and over Ωn K compare. We prove the following discretization of the uniform norm for low-degree polynomials: if f has degree at most d as an analytic polynomial, then ∥ f ∥Tn ≤C(d,K)∥ f ∥Ωn K with C(d,K) independent of dimension n. As a consequence we also obtain a new proof of the Bohnenblust–Hille inequality for functions on products of cyclic groups. Key to our argument is a special class of Fourier multipliers on Ωn K which are L∞ →L∞ bounded independent of dimension when restricted to low-degree polynomials. This class includes projections onto the k-homogeneous parts of low-degree polynomials as well as projections of much finer granularity. 

We conducted an exhaustive analysis combining optical photometry and spectroscopy of the type Ia supernova designated SN 2023xqm. Our observational period spanned from the two weeks preceding to 88 days after theB-band peak luminosity time. We determined the peak brightness in theB-band to be −18.90 ± 0.50 mag, and it is accompanied by a moderately slow decay rate of 0.90 ± 0.07 mag. The maximum quasi-bolometric luminosity was estimated to be 1.52 × 10⁴³erg s⁻¹and correlated with a calculated⁵⁶Ni mass of 0.74 ± 0.05M_⊙, aligning with the modestly reduced rate of light curve decay. A plateau that can be observed in ther − icolor curve might correlate with the minor elevation noted between the principal and secondary peaks of thei-band light curve. An initial spectral analysis of SN 2023xqm revealed distinct high-velocity features (HVFs) in Ca IIthat contrast with the subdued HVFs observed in Si II. Such attributes may stem from variations in ionization or temperature or from scenarios involving enhanced element abundance, suggesting a naturally lower photospheric temperature for SN 2023xqm, which could be indicative of incomplete burning during the white dwarf’s detonation. The observed traits in the light curve and the spectral features offer significant insights into the variability among type Ia supernovae and their explosion dynamics. 

Recent efforts in Analysis of Boolean Functions aim to extend core results to new spaces, including to the slice binom([n],k), the hypergrid [K]ⁿ, and noncommutative spaces (matrix algebras). We present here a new way to relate functions on the hypergrid (or products of cyclic groups) to their harmonic extensions over the polytorus. We show the supremum of a function f over products of the cyclic group {exp(2π i k/K)}_{k = 1}^K controls the supremum of f over the entire polytorus ({z ∈ ℂ:|z| = 1}ⁿ), with multiplicative constant C depending on K and deg(f) only. This Remez-type inequality appears to be the first such estimate that is dimension-free (i.e., C does not depend on n). This dimension-free Remez-type inequality removes the main technical barrier to giving 𝒪(log n) sample complexity, polytime algorithms for learning low-degree polynomials on the hypergrid and low-degree observables on level-K qudit systems. In particular, our dimension-free Remez inequality implies new Bohnenblust-Hille-type estimates which are central to the learning algorithms and appear unobtainable via standard techniques. Thus we extend to new spaces a recent line of work [Eskenazis and Ivanisvili, 2022; Huang et al., 2022; Volberg and Zhang, 2023] that gave similarly efficient methods for learning low-degree polynomials on the hypercube and observables on qubits. An additional product of these efforts is a new class of distributions over which arbitrary quantum observables are well-approximated by their low-degree truncations - a phenomenon that greatly extends the reach of low-degree learning in quantum science [Huang et al., 2022]. 

Abstract SN 2023ehl, a normal Type Ia supernova with a typical decline rate, was discovered in the galaxy UGC 11555 and offers valuable insights into the explosion mechanisms of white dwarfs. We present a detailed analysis of SN 2023ehl, including spectroscopic and photometric observations. The supernova exhibits high-velocity features in its ejecta, which are crucial for understanding the physical processes during the explosion. We compared the light curves of SN 2023ehl with other well-observed Type Ia supernovae, finding similarities in their evolution. The line strength ratioR(Siii) was calculated to be 0.17 ± 0.04, indicating a higher photospheric temperature compared to other supernovae. The maximum quasi-bolometric luminosity was determined to be 1.52 × 10⁴³erg s⁻¹, and the synthesized⁵⁶Ni mass was estimated at 0.77 ± 0.05M_⊙. The photospheric velocity atB-band maximum light was measured as 10,150 ± 240 km s⁻¹, classifying SN 2023ehl as a normal velocity Type Ia supernova. Our analysis suggests that SN 2023ehl aligns more with both the gravitationally confined detonation, providing a comprehensive view of the diversity and complexity of Type Ia supernovae. 

During mitosis, cells round up and utilize the interphase adhesion sites within the fibrous extracellular matrix (ECM) as guidance cues to orient the mitotic spindles. Here, using suspended ECM-mimicking nanofiber networks, we explore mitotic outcomes and error distribution for various interphase cell shapes. Elongated cells attached to single fibers through two focal adhesion clusters (FACs) at their extremities result in perfect spherical mitotic cell bodies that undergo significant 3-dimensional (3D) displacement while being held by retraction fibers (RFs). Increasing the number of parallel fibers increases FACs and retraction fiber-driven stability, leading to reduced 3D cell body movement, metaphase plate rotations, increased interkinetochore distances, and significantly faster division times. Interestingly, interphase kite shapes on a crosshatch pattern of four fibers undergo mitosis resembling single-fiber outcomes due to rounded bodies being primarily held in position by RFs from two perpendicular suspended fibers. We develop a cortex–astral microtubule analytical model to capture the retraction fiber dependence of the metaphase plate rotations. We observe that reduced orientational stability, on single fibers, results in increased monopolar mitotic defects, while multipolar defects become dominant as the number of adhered fibers increases. We use a stochastic Monte Carlo simulation of centrosome, chromosome, and membrane interactions to explain the relationship between the observed propensity of monopolar and multipolar defects and the geometry of RFs. Overall, we establish that while bipolar mitosis is robust in fibrous environments, the nature of division errors in fibrous microenvironments is governed by interphase cell shapes and adhesion geometries. 

Ovarian cancer is routinely diagnosed long after the disease has metastasized through the fibrous submesothelium. Despite extensive research in the field linking ovarian cancer progression to increasingly poor prognosis, there are currently no validated cellular markers or hallmarks of ovarian cancer that can predict metastatic potential. To discern disease progression across a syngeneic mouse ovarian cancer progression model, here we fabricated extracellular matrix mimicking suspended fiber networks: cross-hatches of mismatch diameters for studying protrusion dynamics, aligned same diameter networks of varying interfiber spacing for studying migration, and aligned nanonets for measuring cell forces. We found that migration correlated with disease while a force-disease biphasic relationship exhibited F-actin stress fiber network dependence. However, unique to suspended fibers, coiling occurring at the tips of protrusions and not the length or breadth of protrusions displayed the strongest correlation with metastatic potential. To confirm that our findings were more broadly applicable beyond the mouse model, we repeated our studies in human ovarian cancer cell lines and found that the biophysical trends were consistent with our mouse model results. Altogether, we report complementary high throughput and high content biophysical metrics capable of identifying ovarian cancer metastatic potential on a timescale of hours.