Binding of Polarons and Atoms at Threshold

If the polaron coupling constant $\alpha$ is large enough, bipolarons or multi-polarons will form. When passing through the critical $\alpha_c$ from above, does the radius of the system simply get arbitrarily large or does it reach a maximum and then explodes? We prove that it is always the latter. We also prove the analogous statement for the Pekar-Tomasevich (PT) approximation to the energy, in which case there is a solution to the PT equation at $\alpha_c$. Similarly, we show that the same phenomenon occurs for atoms, e.g., helium, at the critical value of the nuclear charge. Our proofs rely only on energy estimates, not on a detailed analysis of the Schr\"odinger equation, and are very general. They use the fact that the Coulomb repulsion decays like $1/r$, while `uncertainty principle' localization energies decay more rapidly, as $1/r^2$.Comment: 19 page

Grand challenges in evolutionary developmental biology

EVO-DEVO'S IDENTITY There is a widespread consensus on the view that evolutionary developmental biology (evo-devo) is the discipline eventually borne to fill the gap between evolutionary biology and developmental biology, following a divorce between these two fields that extended over more than half a century (Amundson, 2005). On closer inspection, however, this broadly acceptable perspective discloses a wealth of questions, if looked at retrospectively, and of potentially divergent possibilities, if looked at prospectively. The slow pace of integration between the different threads that were converging into evo-devo was well expressed by Raff (2000) in a survey of the main issues in this field. Some 15 years ago Raff, one of the discipline's founding fathers, remarked that "What constitutes the fundamental problems for a science of evolutionary developmental biology (evo-devo) depends on whether the scientist is a developmental biologist, a paleontologist or an evolutionary biologist" and drafted a list of at the time hot issues. Evo-devo has answered these questions only in part. However, this discipline is now mature for addressing a number of more precise, and more challenging questions, as I will argue in this article. To date, two sets of problems have been primarily floated in discussions about the identity and research targets of evo-devo. On the one hand are those centered around the (controversial) notions of evolvability, robustness and constraint in connection with the increasing appreciation of the intricacies of the genotype→phenotype map (Alberch, 1991; Altenberg, 1995; West-Eberhard, 2003; Pigliucci, 2010; Wagner and Zhang, 2011). On the other hand are those centered around the notions of origination, innovation, and novelty, the so-called "innovation triad." To Hendrikse et al. (2007), for example, evolvability is the key issue that justifies recognizing evo-devo as an autonomous discipline. Others, e.g., Muller and Newman (2005), focus instead on the innovation triad. Unfortunately, for all these candidates to core concept of evo-devo, too many alternative definitions have been proposed (or, more dangerously, implicitly assumed), thus adding new items to the dramatically increasing series of biological terms on whose definition there seem to be more and more disagreement. Eventually, we should probably learn to accept that multiple notions associated with each of these terms deserve to be retained and perhaps recognized by adjectival specifications. Similar terminological refinement is applied to other biological terms such as species (e.g., Claridge et al., 1997), homology (e.g., Minelli and Fusco, 2013a), and gene (e.g., Beurton et al., 2000). In discussing the concept of gene in historical perspective, Muller-Wille and Rheinberger (2009) have sensibly recalled Friedrich Nietzsche's (1887; second essay, para. 13) dictum, that "all concepts in which an entire process is semiotically concentrated elude definition; only that which has no history is definable." In addition to terminological ambiguity, there is an another problem with the "innovation triad"—the problem that these terms are all framed in terms of "origins." Framing definitions in terms of origin requires splitting the evolutionary sequence in two contiguous segments, "before" and "after" the origination of a new feature. This splitting is a natural consequence if origination indeed "refers to the specific causality of the generative conditions that underlie both the first origins and the later innovations of phenotypes" and especially "the very first beginnings of phenotypes, e.g., the origin of multicellular assemblies, of complex tissues, and of the generic forms that result from the self-organizational and physical principles of cell interaction (Newman, 1992, 1994). In contrast, innovation [evolutionary modes and mechanisms] and novelty [their phenotypic outcome] designate the processes and results of introducing new characters into already existing phenotypic themes of a certain architecture (bodyplans)" (Muller and Newman, 2005, p. 490). This separation, however, is artificial. The better we know a process, the less we are able to identify its exact origins, these instead being determined by arbitrary choice. In science, and especially in biological disciplines with a strong historical dimension such as evolutionary biology and developmental biology, we should frame questions in terms of transitions rather than origins

Life, time, and the organism:Temporal registers in the construction of life forms

In this paper, we articulate how time and temporalities are involved in the making of living things. For these purposes, we draw on an instructive episode concerning Norfolk Horn sheep. We attend to historical debates over the nature of the breed, whether it is extinct or not, and whether presently living exemplars are faithful copies of those that came before. We argue that there are features to these debates that are important to understanding contemporary configurations of life, time and the organism, especially as these are articulated within the field of synthetic biology. In particular, we highlight how organisms are configured within different material and semiotic assemblages that are always structured temporally. While we identify three distinct structures, namely the historical, phyletic and molecular registers, we do not regard the list as exhaustive. We also highlight how these structures are related to the care and value invested in the organisms at issue. Finally, because we are interested ultimately in ways of producing time, our subject matter requires us to think about historiographical practice reflexively. This draws us into dialogue with other scholars interested in time, not just historians, but also philosophers and sociologists, and into conversations with them about time as always multiple and never an inert background

Robustness and autonomy in biological systems: how regulatory mechanisms enable functional integration, complexity and minimal cognition through the action of second-order control constraints

Living systems employ several mechanisms and behaviors to achieve robustness and maintain themselves under changing internal and external conditions. Regulation stands out from them as a specific form of higher-order control, exerted over the basic regime responsible for the production and maintenance of the organism, and provides the system with the capacity to act on its own constitutive dynamics. It consists in the capability to selectively shift between different available regimes of self-production and self-maintenance in response to specific signals and perturbations, due to the action of a dedicated subsystem which is operationally distinct from the regulated ones. The role of regulation, however, is not exhausted by its contribution to maintain a living system’s viability. While enhancing robustness, regulatory mechanisms play a fundamental role in the realization of an autonomous biological organization. Specifically, they are at the basis of the remarkable integration of biological systems, insofar as they coordinate and modulate the activity of distinct functional subsystems. Moreover, by implementing complex and hierarchically organized control architectures, they allow for an increase in structural and organizational complexity while minimizing fragility. Finally, they endow living systems, from their most basic unicellular instances, with the capability to control their own internal dynamics to adaptively respond to specific features of their interaction with the environment, thus providing the basis for the emergence of minimal forms of cognition