Potentiality in Biology

We take the potentialities that are studied in the biological sciences (e.g., totipotency) to be an important subtype of biological dispositions. The goal of this paper is twofold: first, we want to provide a detailed understanding of what biological dispositions are. We claim that two features are essential for dispositions in biology: the importance of the manifestation process and the diversity of conditions that need to be satisfied for the disposition to be manifest. Second, we demonstrate that the concept of a disposition (or potentiality) is a very useful tool for the analysis of the explanatory practice in the biological sciences. On the one hand it allows an in-depth analysis of the nature and diversity of the conditions under which biological systems display specific behaviors. On the other hand the concept of a disposition may serve a unificatory role in the philosophy of the natural sciences since it captures not only the explanatory practice of biology, but of all natural sciences. Towards the end we will briefly come back to the notion of a potentiality in biology

A Rational and Efficient Algorithm for View Revision in Databases

The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In this paper, we argue that to apply rationality result of belief dynamics theory to various practical problems, it should be generalized in two respects: first of all, it should allow a certain part of belief to be declared as immutable; and second, the belief state need not be deductively closed. Such a generalization of belief dynamics, referred to as base dynamics, is presented, along with the concept of a generalized revision algorithm for Horn knowledge bases. We show that Horn knowledge base dynamics has interesting connection with kernel change and abduction. Finally, we also show that both variants are rational in the sense that they satisfy certain rationality postulates stemming from philosophical works on belief dynamics

On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses

We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model where spikes are effective at times multiple of a characteristic time scale $\delta$, where $\delta$ can be \textit{arbitrary} small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and Integrate-and-Fire models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.Comment: 36 pages, 9 figure

Generalized trace distance measure connecting quantum and classical non-Markovianity

We establish a direct connection of quantum Markovianity of an open quantum system to its classical counterpart by generalizing the criterion based on the information flow. Here, the flow is characterized by the time evolution of Helstrom matrices, given by the weighted difference of statistical operators, under the action of the quantum dynamical evolution. It turns out that the introduced criterion is equivalent to P-divisibility of a quantum process, namely divisibility in terms of positive maps, which provides a direct connection to classical Markovian stochastic processes. Moreover, it is shown that similar mathematical representations as those found for the original trace distance based measure hold true for the associated, generalized measure for quantum non-Markovianity. That is, we prove orthogonality of optimal states showing a maximal information backflow and establish a local and universal representation of the measure. We illustrate some properties of the generalized criterion by means of examples.Comment: 11 pages, 3 figure

Robust Implementation in Direct Mechanisms

A social choice function is robustly implementable if there is a mechanism under which the process of iteratively eliminating strictly dominated messages leads to outcomes that agree with the social choice function for all beliefs at every type profile. In an interdependent value envi­ronment with single crossing preferences, we identify a contraction property on the preferences which together with strict ex post incentive compatibility is sufficient to guarantee robust imple­mentation in the direct mechanism. Strict ex post incentive compatibility and the contraction property are also necessary for robust implementation in any mechanism, including indirect ones. The contraction property requires that the interdependence is not too large. In a linear signal model, the contraction property is equivalent to an interdependence matrix having all eigenvalues smaller than one.Mechanism design, Implementation, Robustness, Common knowledge, Interim equilibrium, Iterative deletion, Direct mechanism

Neutrino mixing, interval matrices and singular values

We study the properties of singular values of mixing matrices embedded within an experimentally determined interval matrix. We argue that any physically admissible mixing matrix needs to have the property of being a contraction. This condition constrains the interval matrix, by imposing correlations on its elements and leaving behind only physical mixings that may unveil signs of new physics in terms of extra neutrino species. We propose a description of the admissible three-dimensional mixing space as a convex hull over experimentally determined unitary mixing matrices parametrized by Euler angles which allows us to select either unitary or nonunitary mixing matrices. The unitarity-breaking cases are found through singular values and we construct unitary extensions yielding a complete theory of minimal dimensionality larger than three through the theory of unitary matrix dilations. We discuss further applications to the quark sector.Comment: Misprints correcte