Active Mass Under Pressure

After a historical introduction to Poisson's equation for Newtonian gravity, its analog for static gravitational fields in Einstein's theory is reviewed. It appears that the pressure contribution to the active mass density in Einstein's theory might also be noticeable at the Newtonian level. A form of its surprising appearance, first noticed by Richard Chase Tolman, was discussed half a century ago in the Hamburg Relativity Seminar and is resolved here.Comment: 28 pages, 4 figure

Facts, Norms and Expected Utility Functions

International audienceIn this paper we want to explore an argumentative pattern that provides a normative justification for expected utility functions grounded on empirical evidence, showing how it worked in three different episodes of their development. The argument claims that we should prudentially maximize our expected utility since this is the criterion effectively applied by those who are considered wisest in making risky choices (be it gamblers or businessmen). Yet, to justify the adoption of this rule, it should be proven that this is empirically true: i.e., that a given function allows us to predict the choices of that particular class of agents. We show how expected utility functions were introduced and contested in accordance to this pattern in the 18th century and how it recurred in the 1950s when M. Allais made his case against the neobernoullians

A nonparametric urn-based approach to interacting failing systems with an application to credit risk modeling

In this paper we propose a new nonparametric approach to interacting failing systems (FS), that is systems whose probability of failure is not negligible in a fixed time horizon, a typical example being firms and financial bonds. The main purpose when studying a FS is to calculate the probability of default and the distribution of the number of failures that may occur during the observation period. A model used to study a failing system is defined default model. In particular, we present a general recursive model constructed by the means of inter- acting urns. After introducing the theoretical model and its properties we show a first application to credit risk modeling, showing how to assess the idiosyncratic probability of default of an obligor and the joint probability of failure of a set of obligors in a portfolio of risks, that are divided into reliability classes

Anomalous Behavior of the Contact Process with Aging

The effect of power-law aging on a contact process is studied by simulation and using a mean-field approach. We find that the system may approach its stationary state in a nontrivial, nonmonotonous way. For the particular value of the aging exponent, $\alpha=1$, we observe a rich set of behaviors: depending on the process parameters, the relaxation to the stationary state proceeds as $1/\ln t$ or via a power law with a nonuniversal exponent. Simulation results suggest that for $0<\alpha<1$, the absorbing-state phase transition is in the universality class of directed percolation.Comment: 4 pages revtex (twocolumn, psfig), 3 figure

U and Th content in the Central Apennines continental crust: a contribution to the determination of the geo-neutrinos flux at LNGS

The regional contribution to the geo-neutrino signal at Gran Sasso National Laboratory (LNGS) was determined based on a detailed geological, geochemical and geophysical study of the region. U and Th abundances of more than 50 samples representative of the main lithotypes belonging to the Mesozoic and Cenozoic sedimentary cover were analyzed. Sedimentary rocks were grouped into four main "Reservoirs" based on similar paleogeographic conditions and mineralogy. Basement rocks do not outcrop in the area. Thus U and Th in the Upper and Lower Crust of Valsugana and Ivrea-Verbano areas were analyzed. Based on geological and geophysical properties, relative abundances of the various reservoirs were calculated and used to obtain the weighted U and Th abundances for each of the three geological layers (Sedimentary Cover, Upper and Lower Crust). Using the available seismic profile as well as the stratigraphic records from a number of exploration wells, a 3D modelling was developed over an area of 2^{\circ}x2^{\circ} down to the Moho depth, for a total volume of about 1.2x10^6 km^3. This model allowed us to determine the volume of the various geological layers and eventually integrate the Th and U contents of the whole crust beneath LNGS. On this base the local contribution to the geo-neutrino flux (S) was calculated and added to the contribution given by the rest of the world, yielding a Refined Reference Model prediction for the geo-neutrino signal in the Borexino detector at LNGS: S(U) = (28.7 \pm 3.9) TNU and S(Th) = (7.5 \pm 1.0) TNU. An excess over the total flux of about 4 TNU was previously obtained by Mantovani et al. (2004) who calculated, based on general worldwide assumptions, a signal of 40.5 TNU. The considerable thickness of the sedimentary rocks, almost predominantly represented by U- and Th- poor carbonatic rocks in the area near LNGS, is responsible for this difference.Comment: 45 pages, 5 figures, 12 tables; accepted for publication in GC

Under pressure: Response urgency modulates striatal and insula activity during decision-making under risk

When deciding whether to bet in situations that involve potential monetary loss or gain (mixed gambles), a subjective sense of pressure can influence the evaluation of the expected utility associated with each choice option. Here, we explored how gambling decisions, their psychophysiological and neural counterparts are modulated by an induced sense of urgency to respond. Urgency influenced decision times and evoked heart rate responses, interacting with the expected value of each gamble. Using functional MRI, we observed that this interaction was associated with changes in the activity of the striatum, a critical region for both reward and choice selection, and within the insula, a region implicated as the substrate of affective feelings arising from interoceptive signals which influence motivational behavior. Our findings bridge current psychophysiological and neurobiological models of value representation and action-programming, identifying the striatum and insular cortex as the key substrates of decision-making under risk and urgency

Linear frictional forces cause orbits to neither circularize nor precess

For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge-Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure to damped systems suggested recently by Tarasov[1]. In this generalized algebraic structure the orbit-averaged Runge-Lenz vector remains a constant in the linearly damped Kepler problem to leading order in the damping coeComment: 16 pages. 1 figure, Rewrite for resubmissio

How brains make decisions

This chapter, dedicated to the memory of Mino Freund, summarizes the Quantum Decision Theory (QDT) that we have developed in a series of publications since 2008. We formulate a general mathematical scheme of how decisions are taken, using the point of view of psychological and cognitive sciences, without touching physiological aspects. The basic principles of how intelligence acts are discussed. The human brain processes involved in decisions are argued to be principally different from straightforward computer operations. The difference lies in the conscious-subconscious duality of the decision making process and the role of emotions that compete with utility optimization. The most general approach for characterizing the process of decision making, taking into account the conscious-subconscious duality, uses the framework of functional analysis in Hilbert spaces, similarly to that used in the quantum theory of measurements. This does not imply that the brain is a quantum system, but just allows for the simplest and most general extension of classical decision theory. The resulting theory of quantum decision making, based on the rules of quantum measurements, solves all paradoxes of classical decision making, allowing for quantitative predictions that are in excellent agreement with experiments. Finally, we provide a novel application by comparing the predictions of QDT with experiments on the prisoner dilemma game. The developed theory can serve as a guide for creating artificial intelligence acting by quantum rules.Comment: Latex file, 20 pages, 3 figure

The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological systems, but formal treatments face the problem of defining a quantitative measure of information rooted in a concept of fitness, which is itself an elusive notion. Here, we present a model of population dynamics where this problem is amenable to a mathematical analysis. In the limit where any information about future environmental variations is common to the members of the population, our model is equivalent to known models of financial investment. In this case, the population can be interpreted as a portfolio of financial assets and previous analyses have shown that a key quantity of Shannon's communication theory, the mutual information, sets a fundamental limit on the value of information. We show that this bound can be violated when accounting for features that are irrelevant in finance but inherent to biological systems, such as the stochasticity present at the individual level. This leads us to generalize the measures of uncertainty and information usually encountered in information theory

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request