The aim of this work is twofold. First, we survey the techniques developed in Perthame and Zubelli (Inverse Probl 23(3):1037–1052, 2007 ), Doumic et al. (Inverse Probl 25, 2009 ) to reconstruct the division (birth) rate from the cell volume distribution data in certain structured population structured population models. Secondly, we implement such techniques on experimental cell volume distributions available in the literature so as to validate the theoretical and numerical results. As a proof of concept, we use the experimental (...) data experimental data reported in the classical work of Kubitschek (Biophys J 9(6):792–809, 1969 ) concerning Escherichia coli in vitro experiments measured by means of a Coulter transducer-multichannel analyzer system (Coulter Electronics, Inc., Hialeah, FL, USA). Despite the rather old measurement technology, the reconstructed division rates still display potentially useful biological features. (shrink)

In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...) axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is U×U for some set U) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares. (shrink)

In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational (...) axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is ᵎ x ᵎ for some set ᵎ) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares. (shrink)

When visual attention is directed away from a stimulus, neural processing is weak and strength and precision of sensory data decreases. From a computational perspective, in such situations observers should give more weight to prior expectations in order to behave optimally during a discrimination task. Here we test a signal detection theoretic model that counter-intuitively predicts subjects will do just the opposite in a discrimination task with two stimuli, one attended and one unattended: when subjects are probed to discriminate the (...) unattended stimulus, they rely less on prior information about the probed stimulus’ identity. The model is in part inspired by recent findings that attention reduces trial-by-trial variability of the neuronal population response and that they use a common criterion for attended and unattended trials. In five different visual discrimination experiments, when attention was directed away from the target stimulus, subjects did not adjust their response bias in reaction to a change in stimulus presentation frequency despite being fully informed and despite the presence of performance feedback and monetary and social incentives. This indicates that subjects did not rely more on the priors under conditions of inattention as would be predicted by a Bayes-optimal observer model. These results inform and constrain future models of Bayesian inference in the human brain. (shrink)

The idea that natural selection acts on many levels—and not only at the level of organisms or individual genes—is increasingly accepted among biologists. However, it is not easy to reconcile this idea with the strictly “individualistic” conception of the evolutionary process that has always characterized Darwinian thought. Moreover, the individuality of some forms of life is a vague concept and therefore controversial. This is the case of Candidatus Magnetoglobus multicellularis, whose discovery immediately inspired the following question: Does the concept of (...) individuality have degrees? Alternatively, how far is this structure of prokaryotic cells from deserving to be called an organism? In this article, we propose a new conceptual scheme based on an idea of individuality that is not limited to organisms and that makes sense in terms of Darwinian evolution. In this conceptual scheme, selection at levels above that of the individual organism is interpreted as the evolutionary emergence of higher-level individuality. This proposal may serve as a basis on which to construct a promising hierarchical evolutionary theory. (shrink)

The idea that natural selection acts on many levels—and not only at the level of organisms or individual genes—is increasingly accepted among biologists. However, it is not easy to reconcile this idea with the strictly “individualistic” conception of the evolutionary process that has always characterized Darwinian thought. Moreover, the individuality of some forms of life is a vague concept and therefore controversial. This is the case of Candidatus Magnetoglobus multicellularis, whose discovery immediately inspired the following question: Does the concept of (...) individuality have degrees? Alternatively, how far is this structure of prokaryotic cells from deserving to be called an organism? In this article, we propose a new conceptual scheme based on an idea of individuality that is not limited to organisms and that makes sense in terms of Darwinian evolution. In this conceptual scheme, selection at levels above that of the individual organism is interpreted as the evolutionary emergence of higher-level individuality. This proposal may serve as a basis on which to construct a promising hierarchical evolutionary theory. (shrink)