Countability properties of some Berkovich spaces

We prove that any compact Berkovich space over the field of Laurent series over an arbitrary field is angelic. In particular, is it sequentially compact.Comment: 11 page

Equitable Self-Ownership for Animals

This Article proposes a new use of existing property law concepts to change the juristic personhood status of animals. Presently, animals are classified as personal property, which gives them no status or standing in the legal system for the protection or promotion of their interests. Professor Favre suggest that it is possible and appropriate to divide living property into its legal and equitable components, and then to transfer the equitable title of an animal from the legal title holder to the animal herself. This would create a new, limited form of self-ownership in an animal, an equitably self-owned animal. Such a new status would have two primary impacts. First, the animal would have access to the legal system, at least in what has historically been the realm of equity, for the protection and assertion of his or her interests. Secondly, the human holder of legal title will, like a traditional trustee, have obligations to the equitable owner of the animal, that is the animal himself. As the subject matter of this trust-like relationship would be a living being, not money or wealth, the legal owner would best be characterized as a guardian, rather than by the traditional category of trustee. The Article concludes with a short discussion of the use of anti-cruelty law and human guardianship concepts as providing a context for the further development of this new concept of equitable self-ownership

On a Navier-Stokes-Allen-Cahn model with inertial effects

A mathematical model describing the flow of two-phase fluids in a bounded container $\Omega$ is considered under the assumption that the phase transition process is influenced by inertial effects. The model couples a variant of the Navier-Stokes system for the velocity $u$ with an Allen-Cahn-type equation for the order parameter $\varphi$ relaxed in time in order to introduce inertia. The resulting model is characterized by second-order material derivatives which constitute the main difficulty in the mathematical analysis. Actually, in order to obtain a tractable problem, a viscous relaxation term is included in the phase equation. The mathematical results consist in existence of weak solutions in 3D and, under additional assumptions, existence and uniqueness of strong solutions in 2D. A partial characterization of the long-time behavior of solutions is also given and in particular some issues related to dissipation of energy are discussed.Comment: 24 page

Continuity of the Green function in meromorphic families of polynomials

We prove that along any marked point the Green function of a meromorphic family of polynomials parameterized by the punctured unit disk explodes exponentially fast near the origin with a continuous error term.Comment: Modified references. Added a corollary about the adelic metric associated with an algebraic family endowed with a marked poin

A generic model of dyadic social relationships

We introduce a model of dyadic social interactions and establish its correspondence with relational models theory (RMT), a theory of human social relationships. RMT posits four elementary models of relationships governing human interactions, singly or in combination: Communal Sharing, Authority Ranking, Equality Matching, and Market Pricing. To these are added the limiting cases of asocial and null interactions, whereby people do not coordinate with reference to any shared principle. Our model is rooted in the observation that each individual in a dyadic interaction can do either the same thing as the other individual, a different thing or nothing at all. To represent these three possibilities, we consider two individuals that can each act in one out of three ways toward the other: perform a social action X or Y, or alternatively do nothing. We demonstrate that the relationships generated by this model aggregate into six exhaustive and disjoint categories. We propose that four of these categories match the four relational models, while the remaining two correspond to the asocial and null interactions defined in RMT. We generalize our results to the presence of N social actions. We infer that the four relational models form an exhaustive set of all possible dyadic relationships based on social coordination. Hence, we contribute to RMT by offering an answer to the question of why there could exist just four relational models. In addition, we discuss how to use our representation to analyze data sets of dyadic social interactions, and how social actions may be valued and matched by the agents

Event detection, tracking, and visualization in Twitter: a mention-anomaly-based approach

The ever-growing number of people using Twitter makes it a valuable source of timely information. However, detecting events in Twitter is a difficult task, because tweets that report interesting events are overwhelmed by a large volume of tweets on unrelated topics. Existing methods focus on the textual content of tweets and ignore the social aspect of Twitter. In this paper we propose MABED (i.e. mention-anomaly-based event detection), a novel statistical method that relies solely on tweets and leverages the creation frequency of dynamic links (i.e. mentions) that users insert in tweets to detect significant events and estimate the magnitude of their impact over the crowd. MABED also differs from the literature in that it dynamically estimates the period of time during which each event is discussed, rather than assuming a predefined fixed duration for all events. The experiments we conducted on both English and French Twitter data show that the mention-anomaly-based approach leads to more accurate event detection and improved robustness in presence of noisy Twitter content. Qualitatively speaking, we find that MABED helps with the interpretation of detected events by providing clear textual descriptions and precise temporal descriptions. We also show how MABED can help understanding users' interest. Furthermore, we describe three visualizations designed to favor an efficient exploration of the detected events.Comment: 17 page

The dynamical Manin-Mumford problem for plane polynomial automorphisms

Let $f$ be a polynomial automorphism of the affine plane. In this paper we consider the possibility for it to possess infinitely many periodic points on an algebraic curve $C$. We conjecture that this happens if and only if $f$ admits a time-reversal symmetry; in particular the Jacobian $\mathrm{Jac}(f)$ must be a root of unity. As a step towards this conjecture, we prove that the Jacobian of $f$ and all its Galois conjugates lie on the unit circle in the complex plane. Under mild additional assumptions we are able to conclude that indeed $\mathrm{Jac}(f)$ is a root of unity. We use these results to show in various cases that any two automorphisms sharing an infinite set of periodic points must have a common iterate, in the spirit of recent results by Baker-DeMarco and Yuan-Zhang.Comment: 45 pages. Theorems A and B are now extended to automorphisms defined over any field of characteristic zer

The impact of immigration on the wage distribution in Switzerland

Recent immigrants in Switzerland are overrepresented at the top of the wage distribution in high and at the bottom in low skill occupations. Basic economic theory thus suggests that immigration has led to a compression of the wage distribution in the former group and to an expansion in the latter. The data confirm this proposition for high skill occupations, but reveal effects close to zero for low skill occupations. While the estimated wage effects are of considerable magnitude at the tails of the wage distribution in high skill occupations, the effects on overall inequality are shown to be negligible.Immigration, wage distribution, occupation groups, inequality