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This review explores the physical mechanisms driving the evolution of low- and intermediate-mass binary star systems, with particular emphasis on emerging mechanisms that challenge classical paradigms. We begin by describing the principal formation channels and orbital properties of binary systems. A critical reassessment of the Roche lobe formalism is presented, focusing on systems with eccentric orbits and asynchronous rotation, where deviations from traditional approximations become significant. We then review current theoretical models of mass and angular momentum exchange via Roche-lobe overflow, incorporating results from recent hydrodynamical simulations of wind accretion. The review also reports advances in tidal dissipation theory. Finally, we explore mechanisms capable of sustaining or exciting orbital eccentricity, including perturbations induced by mass transfer and interactions with circumbinary disks. These discussions aim to outline underexplored facets of binary evolution, offering new perspectives for theoretical and observational studies.

We consider how flat a lattice simplex contained in the hypercube $[0,k]^d$ can be. This question is related to the notion of kissing polytopes: two lattice polytopes contained in the hypercube $[0,k]^d$ are kissing when they are disjoint but their distance is as small as possible. We show that the smallest possible distance of a lattice point $P$ contained in the cube $[0,k]^3$ to a lattice triangle in the same cube that does not contain $P$ is $$ \frac{1}{\sqrt{3k^4-4k^3+4k^2-2k+1}} $$ when $k$ is at least $2$. We also improve the known lower bounds on the distance of kissing polytopes for $d$ at least $4$ and $k$ at least $2$.

The traditional Triangular Maximally Filtered Graph (TMFG) construction requires pre-computation and storage of a dense correlation matrix; this limits its applicability to small and medium-sized datasets. Here we identify key memory and runtime complexity challenges when using TMFG at scale. We then present the Approximate Triangular Maximally Filtered Graph (a-TMFG) algorithm. This is a novel approach to scaling the construction of artificial graphs from data inspired by TMFG. The method employs k-Nearest Neighbors Graphs (kNNG) for initial construction, and implements a memory management strategy to search and estimate missing correlations on-the-fly. This provides representations to control combinatorial explosion. The algorithm is tested for robustness to the parameters and noise, and is evaluated on datasets with millions of observations. This new method provides a parsimonious way to construct graphs for use-cases where graphs are used as input to supervised and unsupervised learning but where no natural graph exists.

Direct Numerical Simulation of turbulent channel flow at friction Reynolds number around 200 is performed with spanwise wall actuation to achieve drag reduction. A quasi-square-wave waveform, featuring impulsive transitions and constant-velocity plateaus, separates the actuation cycle into distinct Reversal and Displacement Phases, thereby permitting direct observation of the underlying physics. Phase-resolved analysis reveals that the actuation modulates the self-sustaining process (SSP): during the Reversal Phase, the Stokes strain passes through zero, the SSP resumes, and streaks regenerate; during the Displacement Phase, sustained Stokes strain diverts wall-normal vorticity spanwise via vortex tilting, depleting SSP precursors and suppressing streaks. A stochastic enstrophy-budget analysis confirms this mechanism at the governing-equation level: competition between mean-shear production of wall-normal enstrophy and Stokes-driven spanwise diversion, drawing from a shared reservoir, reflects directed, phase-opposed switching. The quasi-square wave improves the gross drag-reduction margin by 2.5 percentage points over the optimal sinusoidal baseline, solely via temporal Stokes-str

The formation of the most massive quasars observed at high redshifts requires extreme accretion rates ($>1$ M$_\odot$ yr$^{-1}$). Inflows of $10-1000$ M$_\odot$ yr$^{-1}$ are found in hydrodynamical simulations of galaxy mergers, leading to the formation of supermassive discs (SMDs) with high metallicities ($>$ Z$_\odot$). Supermassive stars (SMSs) born in these SMDs could be the progenitors of the most extreme quasars. Here, we study the properties of non-rotating SMSs forming in high metallicity SMDs. Using the stellar evolution code GENEC, we compute numerically the hydrostatic structures of non-rotating SMSs with metallicities $Z=1-10$ Z$_\odot$ by following their evolution under constant accretion at rates $10-1000$ M$_\odot$ yr$^{-1}$. We determine the final mass of the SMSs, set by the general-relativistic (GR) instability, by applying the relativistic equation of adiabatic pulsations to the hydrostatic structures. We find that non-rotating SMSs with metallicities $Z=1-10$ Z$_\odot$ accreting at rates $10-1000$ M$_\odot$ yr$^{-1}$ evolve as red supergiant protostars until their final collapse. All the models reach the GR instability during H-burning. The final mass is

Consider a non-negative number $t$ and a hyperplane $H$ of $\mathbb{R}^d$ whose distance to the center of the hypercube $[0,1]^d$ is $t$. If $t$ is equal to $0$ and $H$ is orthogonal to a diagonal of $[0,1]^d$, it is known that the $(d-1)$-dimensional volume of $H\cap[0,1]^d$ is a strictly increasing function of $d$ when $d$ is at least $3$. The study of the monotonicity of this volume is extended for $t$ up to above $1/2$ and, when $d$ is large enough, for every non-negative $t$. In particular, a range for $t$ is identified such that this volume is a strictly decreasing function of $d$ over the positive integers. The local extremality of the $(d-1)$-dimensional volume of $H\cap[0,1]^d$ when $H$ is orthogonal to a diagonal of either $[0,1]^d$ or a lower dimensional face is also determined for the same values of $t$. It is shown for instance that when $t$ is above an explicit constant and $d$ is large enough, this volume is always strictly locally maximal when $H$ is orthogonal to a diagonal of $[0,1]^d$. A precise estimate for the convergence rate of the Eulerian numbers to their limit Gaussian behavior is provided along the way.

A scalar product for quasinormal mode solutions to Teukolsky's homogeneous radial equation is presented. Evaluation of this scalar product can be performed either by direct integration, or by evaluation of a confluent hypergeometric functions. The related scalar product will be useful for better understanding analytic solutions to Teukolsky's radial equation, particularly the quasi-normal modes, their potential spatial completeness, and whether the quasi-normal mode overtone excitations may be estimated by spectral decomposition, rather than fitting. With that motivation, the scalar product is applied to confluent Heun polynomials where it is used to derive their peculiar orthogonality and eigenvalue properties. A potentially new relationship is derived between the confluent Heun polynomials' scalar products and eigenvalues. Using these results, it is shown for the first time that Teukolsky's radial equation (and perhaps similar confluent Heun equations) are, in principle, exactly tri-diagonalizable. To this end, "canonical" confluent Heun polynomials are conjectured.

Granger-Geweke causality (GGC) is a powerful and popular method for identifying directed functional (`causal') connectivity in neuroscience. In a recent paper, Stokes and Purdon [1] raise several concerns about its use. They make two primary claims: (1) that GGC estimates may be severely biased or of high variance, and (2) that GGC fails to reveal the full structural/causal mechanisms of a system. However, these claims rest, respectively, on an incomplete evaluation of the literature, and a misconception about what GGC can be said to measure. Here we explain how existing approaches (as implemented, for example, in our popular MVGC software [2,3]) resolve the first issue, and discuss the frequently-misunderstood distinction between functional and effective neural connectivity which underlies Stokes and Purdon's second claim. [1] Patrick A. Stokes and Patrick. L. Purdon (2017), A study of problems encountered in Granger causality analysis from a neuroscience perspective, Proc. Natl. Acad. Sci. USA 114(34):7063-7072. [2] Lionel Barnett and Anil K. Seth (2012), The MVGC Multivariate Granger Causality Matlab toolbox, http://users.sussex.ac.uk/~lionelb/MVGC/ [3] Lionel Barnett and Anil K

Given a rational number $r$ such that $2r$ is not an integer, we prove that $\tan^2(rπ)$ is irrational unless it is equal to $0$, $1$, $3$ or $\frac{1}{3}$, using only basic trigonometry and the Rational Root Theorem. Moreover, we deduce that $\tan(rπ)$, $\cos^2(rπ)$ ans $\cos(rπ)$ are irrational numbers except in usual cases.

Consider the hyperplanes at a fixed distance $t$ from the center of the hypercube $[0,1]^d$. Significant attention has been given to determining the hyperplanes $H$ among these such that the $(d-1)$-dimensional volume of $H\cap[0,1]^d$ is maximal or minimal. In the spirit of a question by Vitali Milman, the corresponding local problem is considered here when $H$ is orthogonal to a diagonal or a sub-diagonal of the hypercube. It is proven in particular that this volume is strictly locally maximal at the diagonals in all dimensions greater than $3$ within a range for $t$ that is asymptotic to $\sqrt{d}/\!\log d$. At lower order sub-diagonals, this volume is shown to be strictly locally maximal when $t$ is close to $0$ and not locally extremal when $t$ is large. This relies on a characterisation of local extremality at the diagonals and sub-diagonals that allows to solve the problem over the whole possible range for $t$ in any fixed, reasonably low dimension.

A new study suggests spacecraft exhaust could quickly contaminate the moon's most scientifically valuable regions, potentially masking ancient clues about how life began on Earth。 Researchers say future lunar missions should consider new ways to reduce and monitor this pollution before it becomes widespread

Scientists at Nanyang Technological University in Singapore have discovered a surprisingly simple way to create exotic light structures called optical skyrmions using a 200-year-old optical effect known as the Poisson spot。 Instead of relying on expensive, highly engineered materials, they simply shine a laser at a tiny circular disc, producing sta

Supermassive stars (SMSs), with masses $>10^5$ M$_\odot$, have been proposed as the possible progenitors of the most extreme supermassive black holes observed at redshifts $z>6-7$. In this scenario ('direct collapse'), a SMS accretes at rates $>0.1$ M$_\odot$ yr$^{-1}$ until it collapses to a black hole via the general-relativistic (GR) instability. Rotation plays a crucial role in the formation of such supermassive black hole seeds. The centrifugal barrier appears as particularly strong in this extreme case of star formation. Moreover, rotation impacts sensitively the stability of SMSs against GR, as well as the subsequent collapse. In particular, it might allow for gravitational wave emission and ultra-long gamma-ray bursts at black hole formation, which represents currently the main observational signatures proposed in the literature for the existence of such objects. Here, I present the latest models of SMSs accounting for accretion and rotation, and discuss some of the open questions and future prospects in this research line.

Meta denies using AI to terminate workers with disabilities and medical problems

NASA's Hubble Space Telescope has captured a spectacular red, white, and blue view of one of the Milky Way's oldest star clusters to celebrate the nation's 250th anniversary。 Hidden within the ancient cluster are clues to how exploding stars helped transform the young universe into one capable of forming planets and, eventually, life

Dark matter may be far more complicated than scientists once believed。 A new study suggests it could consist of at least two different kinds of particles that slowly separate over time, with heavier particles sinking toward the centers of galaxies and lighter ones drifting outward。 This simple idea could explain several puzzling cosmic observations

Conductive ink is painted directly onto the skin in colorful custom designs, drying into working electrodes