The initial insight into the genetic basis of apoptosis, or programmed cell death, was gained from ingenious studies of the roundworm Caenorhabditis elegans (for review, see Horvitz 1999). These studies revealed a linear pathway whereby the products of two genes, designated Ced-3 andCed-4, were necessary and sufficient to trigger the perfectly timed and orchestrated death of 131 preordained cells during development. The relevance of this pathway to higher animals was established by the discovery of apparent mammalian orthologs of these genes and the demonstration that the mammalian Ced-3-related genes encode proteases (designated caspases) whose activities are responsible for the morphological changes characteristic of apoptosis (for review, see Hengartner 2000). The complexity of the apoptotic program began to increase with the discovery of Bcl-2, a gene whose product causes resistance to apoptosis in lymphocytes (Vaux et al. 1988; McDonnell et al. 1989). Bcl-2 was shown to correct partially the phenotype of a C. elegans mutation in Ced-9, a cell survival gene that functions upstream of Ced-4 and Ced-3 (Vaux et al. 1992). This finding suggested an apparent one-for-one correlation between the C. elegans and mammalian proand antiapoptotic pathways. However, this correlation did not explain two observations made in mammalian cells. First, the Bcl-2 protein was found on the membrane of mitochondria, which were not implicated in C. elegans apoptosis; and second, apoptotic changes could be produced in Xenopus laevis oocyte extracts only when a membrane fraction enriched in mitochondria was present (Hockenberry et al. 1990; Newmeyer et al. 1994). The complex role of mitochondria in mammalian cell apoptosis came into focus when biochemical studies identified several mitochondrial proteins that are able to activate cellular apoptotic programs directly (Liu et al. 1996; Susin et al. 1999; Du et al. 2000; Verhagen et al. 2000; Li et al. 2001). Normally, these proteins reside in the intermembrane space of mitochondria. In response to a variety of apoptotic stimuli, they are released to the cytosol and/or the nucleus. They promote apoptosis either by activating caspases and nucleases or by neutralizing cytosolic inhibitors of this process. A complex picture has emerged in which mitochondrial and cytosolic proapoptotic proteins interact with antiapoptotic proteins with each cell’s life or death hanging in the balance. This review summarizes the recent data on the expanding and complex role of mitochondria in apoptosis.
Flow-based generative models have enabled remarkable progress in fast and controllable generation across continuous and discrete state spaces, yet existing parameterizations are constrained to fixed dimensions or fixed sequence lengths. Here, we introduce Expanding Generative Flows (EFlows), which define flows between distributions of increasing dimensionality along an expanding interpolant that grows the state by augmenting it with conditional noise. Building on this construction, we propose Expanding Flow Maps (EFMs), a new class of flow maps that distill the expanding interpolant into efficient few-step generative models. Each EFM factors the map between any two timesteps into two learnable operations: an expand operator, which augments the state space with new coordinates or tokens conditioned on the current state, and a transport map, which pushes the expanded state forward along the interpolant. Composing these operators yields a single map that jointly expands and denoises the state, recovering existing fixed-canvas flows and flow maps as the special case in which the expand operator is the identity. We further extend the framework to the discrete simplex, enabling variable-
We develop the quantum theory of the causal formation of a long-range magnetic field generated by an external current that is instantaneously switched on and subsequently kept constant in time. The resulting non-equilibrium quantum state, describing the expanding magnetic field, is obtained exactly and compared with the corresponding quantum magnetostatic state. In contrast to the magnetostatic case, the expanding solution exhibits a propagating shockwave-like front separating regions where the magnetic field has already been formed from those that remain causally disconnected from the source. We show that although the expanding field locally approaches the magnetostatic field behind the shockwave-like front, the associated quantum systems remain distinct at all times. In particular, we obtain manifestly different results for the energy, photon number, and their fluctuations in expanding and magnetostatic field configurations. Our results are first derived for a general external current and then illustrated with a specific example.
Nonthermal features are ubiquitously observed in electron velocity distribution functions in the solar wind, yet their origin in the collisionless, turbulent, expanding solar-wind plasma remains unclear. We investigate how solar-wind expansion and Alfvénic turbulence jointly generate and regulate these features using the first fully kinetic particle-in-cell simulation of an expanding turbulent plasma under heliospheric conditions. In our setup, expansion-driven weakening of the magnetic field adiabatically cools the plasma perpendicularly to the mean field while leaving the parallel temperature largely unchanged, driving the system toward the firehose-instability threshold. Concurrently, strongly anisotropic turbulence leads to perpendicular heating and the development of nonthermal features. Subsequently, we find that suprathermal electron populations preferentially develop in the parallel direction, forming pronounced power-law tails even under weakly compressive, highly Alfvénic conditions, and persist despite anisotropy regulation by the firehose instability. The preferentially parallel energization suggests the involvement of parallel electric fields or resonant wave--particle
Anomalous diffusion phenomena have been observed in many complex physical and biological systems. One significant advance recently is the physical extension of particle's motion in static medium to uniformly (and even nonuniformly) expanding medium. The dynamic mechanism of particle's motion in the nonuniformly expanding medium has only been investigated in the framework of continuous-time random walk. To study more physical observables and supplement the theory of the expanding medium problems, we characterize the nonuniformly expanding medium with a spatial-temporal dependent scale factor $a(x,t)$, and build the Langevin picture describing the particle's motion in the nonuniformly expanding medium. By introducing a new coordinate, besides of the existing comoving and physical coordinates, we build the relation between the nonuniformly expanding medium and the uniformly expanding one, and further obtain the moments of the comoving and physical coordinates. Both exponential and power-law formed scale factor are considered to uncover the combined effects of the particle's intrinsic diffusion and the nonuniform expansion of medium. Our detailed theoretical analyses and simulations pr
We consider expanding systems with invariant measures that are uniformly expanding everywhere except on a small measure set and show that the limiting statistics of hitting times for zero measure sets are compound Poisson provided the limits for the cluster size distributions exist. This extends previous results from neighbourhoods around single points to neighbourhoods around zero measure sets. The assumptions require the correlations to decay at least polynomially and the non-uniformly expanding part of the iterates of the map also has to satisfy some decay condition. We also require some regularity conditions around the limiting zero measure target set.
We consider the space of smooth gradient expanding Ricci soliton structures on $S^1 \times \mathbb{R}^3$ and $S^2 \times \mathbb{R}^2$ which are invariant under the action of $\text{SO}(3) \times \text{SO}(2)$. In the case of each topology, there exists a $2$-parameter family of cohomogeneity one solitons asymptotic to cones over the link $S^2 \times S^1$, as constructed by Nienhaus-Wink and Buzano-Dancer-Gallaugher-Wang. By analyzing the resultant soliton ODEs, we reconstruct the $2$-parameter families in each case and provide an alternate proof of conicality. Analogous to work of Bamler and Chen, we define a notion of expander degree for these cohomogeneity one solitons through a properness result. We then proceed to calculate this cohomogeneity one expander degree in the cases of the specific topologies.
Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism of particle's motion in expanding medium has only been investigated in the framework of continuous-time random walk. To focus on more diffusion processes and physical observables, we build the Langevin picture of anomalous diffusion in expanding medium, and conduct detailed analyses in the framework of Langevin equation. With the help of a subordinator, both subdiffusion process and superdiffusion process in expanding medium are discussed. We find that the expanding medium with different changing rate (exponential form and power-law form) leads to quite different diffusion phenomena. The particle's intrinsic diffusion behavior also plays an important role. Our detailed theoretical analyses and simulations present a panoramic view of investigating anomalous diffusion in expanding medium under the framework of Langevin equation.
We study the dynamical properties of ball expanding maps, a class of continuous self-maps defined on compact metric spaces. For a ball expanding map, we show that: (1) the set of periodic points is dense in the chain recurrent set; (2) if the topological entropy of the map is zero, then the chain recurrent set is finite; (3) the map has only finitely many chain components; (4) if the space is perfect, then the topological entropy of the map is positive; and (5) if the space is connected, then the map is locally eventually onto and hence mixing. Several examples are also provided.
Motivated by the long-time behavior of Ricci flows that collapse with bounded curvature, we study expanding Ricci solitons with nilpotent symmetry on vector bundles over a closed manifold. We prove that, under mild assumptions that are satisfied by Ricci flow limits, the equations dimension-reduce to the so-called twisted harmonic-Einstein equations. When the base is a surface, we establish a correspondence between solutions of the latter and a class of G-Higgs bundles. This allows us to produce infinite families of new examples that are not locally homogeneous, and in particular to obtain a complete description in dimension 4. We also show that all our examples admit Einstein one-dimensional extensions.
Underluminous Thermonuclear Supernovae (uTSNe) are an emerging class of transient events that resemble classic Supernovae Type Ia, but peak at much lower luminosities. Suspected to be the deflagrations of white dwarfs, they directly link the final stages of low-mass binary star evolution to extragalactic studies that are critical for cosmology. The ability to detect and study uTSNe is limited by the lack of high spatial resolution (<0.1"), wide-field (>10'x10') imaging capabilities in the optical, as well as large-scale segmented-telescope spectroscopic abilities that allow highly dynamic time-critical spectroscopy of short-duration transient events. Neither capability is currently foreseen for the European Southern Observatory and is therefore an excellent candidate for the Expanding Horizons program.
In this paper we study the thermodynamic formalism of strongly transitive endomorphisms $f$, focusing on the set all expanding measures. In case $f$ is a non-flat $C^{1+}$ map defined on a Riemannian manifold, these are invariant probability measures with all its Lyapunov exponents positive. Given a Hölder continuous potential $\varphi$ we prove the uniqueness of the equilibrium state among the space of expanding measures. Moreover, we show that the existence of an expanding measure $μ$ maximizing the entropy on the the space of expanding measures implies the existence and uniqueness of equilibrium state $μ_{\varphi}$ on the space of expanding measures for any Hölder continuous potential $\varphi$ with a small oscillation $\text{osc }\varphi=\sup\varphi-\inf\varphi$. As some applications, we prove that Collet-Eckmann quadratic maps does not admit phase transition for Hölder potential, and show that for Viana maps and every Hölder continuous potential of sufficiently small oscillation has a unique equilibrium state.
Goldreich-Weber solutions constitute a finite-parameter of expanding and collapsing solutions to the mass-critical Euler-Poisson system. Two subclasses of this family correspond to compactly supported density profiles suitably modulated by the dynamic radius of the star that expands at the self-similar rate $λ(t)_{t\to\infty}\sim t^{\frac23}$ and linear rate $λ(t)_{t\to\infty}\sim t$ respectively. We prove two results: any linearly expanding Goldreich-Weber star is nonlinearly stable, while any given self-similarly expanding Goldreich-Weber star is codimension-4 nonlinearly stable against irrotational perturbations. The codimension-4 condition in the latter result is optimal and reflects the presence of 4 unstable directions in the linearised dynamics in self-similar coordinates, which are induced by the conservation of the energy and the momentum. This result can be viewed as a codimension-1 nonlinear stability of the moduli space of self-similarly expanding Goldreich-Weber stars against irrotational perturbations.
The coming decades will see gravitational-wave (GW) astronomy expand decisively into the mHz-Hz frequency range, opening access to a population of compact binaries that are currently invisible or only detectable moments before merger. The Lunar Gravitational Wave Antenna (LGWA) concept is designed to probe this gap, enabling continuous observation of compact binaries over months to years prior to coalescence, and detecting sources inaccessible to both space-based mHz detectors and current ground-based >10 Hz facilities. This new GW window fundamentally alters the landscape of time-domain multi-messenger astronomy. Rather than reacting to mergers after the fact, LGWA enables predictive, scheduled electromagnetic (EM) follow-up, transforming how compact-object mergers, their environments, and their astrophysical channels are studied. However, fully exploiting LGWA discoveries requires EM capabilities that do not exist today and are unlikely to be available by the 2030s, particularly for wide-area, rapid, spectroscopically rich follow-up at optical and near-infrared wavelengths. This White Paper identifies the key science cases enabled by LGWA that motivate new ground-based capabil
Every expanding map on a closed manifold is topologically conjugate to an expanding map on an infra-nilmanifold, but not every infra-nilmanifold admits an expanding map. In this article we give a complete algebraic characterization of the infra-nilmanifolds admitting an expanding map. We show that, just as in the case of Anosov diffeomorphisms, the existence of an expanding map depends only on the rational holonomy representation of the infra-nilmanifold. A similar characterization is also given for the infra-nilmanifolds with a non-trivial self-cover, which corresponds to determining which almost-Bieberbach groups are co-Hopfian. These results provide many new examples of infra-nilmanifolds without non-trivial self-covers or expanding maps.
In this work we treat a famous topic in Ergodic Theory and Dynamical Systems: uniformly expanding maps. We relate regularity of expanding maps and conjugacies with Lyapunov exponents, metric and topological entropies for expanding maps of the circle. In Theorem C, we present a result of rigidity of expanding maps on the torus $\mathbb{T}^2,$ after we naturally generalize it in higher dimensions. Here, we present techniques involving ordinary differential equations to study rigidity problems of expanding maps. Along of this work we provide another proof of a Shub-Sullivan's Theorem, concerning the regularity of the conjugacy between expanding endomorphism of the circle.
In this paper, we consider the question of existence and uniqueness of absolutely continuous invariant measures for expanding $C^1$ maps of the circle. This is a question which arises naturally from results which are known in the case of expanding $C^k$ maps of the circle where $k\geq 2$, or even $C^{1+ε}$ expanding maps of the circle. In these cases, it is known that there exists a unique absolutely continuous invariant probability measure by the so-called `Folklore Theorem'. It follows that this measure is ergodic. It has been shown however that for $C^1$ maps there need not be any such measure. However, this leaves the question of whether there can be more than one such measure for $C^1$ expanding maps of the circle. This is the subject of this paper, and in it, we show that there exists a $C^1$ expanding map of the circle which has more than one absolutely continuous invariant probability measure.
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly expanding maps. Throughout the discussion, we address the question of why different dynamical systems have different rates of decay of correlations and how this may reflect underlying geometrical characteristics of the system. We also give detailed sketches of some results such as the existence of absolutely continuous invariant measures for Markov expanding maps, the construction of induced Markov expanding maps in some one-dimensional maps, and the proof of the fact that such a construction can be carried out for a positive probability set of maps in the quadratic family.
We investigate the expanding and collapsing regions by taking two well-known spherically symmetric spacetimes. For this purpose, the general formalism is developed by using Israel junction conditions for arbitrary spacetimes. This has been used to obtain the surface energy density and the tangential pressure. The minimal pressure provides the gateway to explore the expanding and collapsing regions. We take Minkowski and Kantowski-Sachs spacetimes and use the general formulation to investigate the expanding and collapsing regions of the shell.
In this paper, we show how to expand Euclidean/Hermitian self-orthogonal code preserving their orthogonal property. Our results show that every $k$-dimension Hermitian self-orthogonal code is contained in a $(k+1)$-dimensional Hermitian self-orthogonal code. Also, for $k< n/2-1$, every $[n,k]$ Euclidean self-orthogonal code is contained in an $[n,k+1]$ Euclidean self-orthogonal code. Moreover, for $k=n/2-1$ and $p=2$, we can also fulfill the expanding process. But for $k=n/2-1$ and $p$ odd prime, the expanding process can be fulfilled if and only if an extra condition must be satisfied. We also propose two feasible algorithms on these expanding procedures.