Two Passions in Plato’s Symposium: Diotima’s To Kalon as a Reorientation of Imperialistic Erōs

In this essay, I propose a reading of two contrasting passions, two kinds of erōs, in the "Symposium." On the one hand, there is the imperialistic desire for conquering and possessing that Alcibiades represents; and on the other hand, there is the productive love of immortal wisdom that Diotima represents. It’s not just what Alcibiades says in the Symposium, but also what he symbolizes. Alcibiades gives a speech in honor of Socrates and of his unrequited love for him, but even here Alcibiades recounts his attempted seduction of Socrates as a failed conquest, as an unsuccessful attempt to violently take possession of something that Socrates has within him. Even more importantly, in 416 BCE (the dramatic date of Agathon’s symposium) Alcibiades was soon to encourage his fellow countrymen to set off on the ruinous Sicilian expedition. Alcibiades’s actions behind-the-scenes of the "Symposium" reveal the clearest manifestation of his imperialistic erōs (for political power in Athens). They also constitute some necessary background to the dialogue, which Plato’s Athenian readers would have had in mind. Where else can we catch a glimpse of this disastrous desire? It is best illustrated in Thucydides’s "History." I show that the beginnings of this political passion can already be seen in Pericles’s funeral oration (2.35-46, specifically 2.43.1) and that after Pericles’s death, Alcibiades stokes this erōs to such a fevered pitch that the Athenians agree to launch the tragic venture against Sicily. Opposed to this political passion, is Diotima’s. She tries to reorient this misguided erōs and presents an alternative form of desire for everlasting wisdom (philosophia)

Perfectly secure data aggregation via shifted projections

We study a general scenario where confidential information is distributed among a group of agents who wish to share it in such a way that the data becomes common knowledge among them but an eavesdropper intercepting their communications would be unable to obtain any of said data. The information is modelled as a deck of cards dealt among the agents, so that after the information is exchanged, all of the communicating agents must know the entire deal, but the eavesdropper must remain ignorant about who holds each card. Valentin Goranko and the author previously set up this scenario as the secure aggregation of distributed information problem and constructed weakly safe protocols, where given any card $c$, the eavesdropper does not know with certainty which agent holds $c$. Here we present a perfectly safe protocol, which does not alter the eavesdropper's perceived probability that any given agent holds $c$. In our protocol, one of the communicating agents holds a larger portion of the cards than the rest, but we show how for infinitely many values of $a$, the number of cards may be chosen so that each of the $m$ agents holds more than $a$ cards and less than $2m^2a$

The intuitionistic temporal logic of dynamical systems

A dynamical system is a pair $(X,f)$, where $X$ is a topological space and $f\colon X\to X$ is continuous. Kremer observed that the language of propositional linear temporal logic can be interpreted over the class of dynamical systems, giving rise to a natural intuitionistic temporal logic. We introduce a variant of Kremer's logic, which we denote ${\sf ITL^c}$, and show that it is decidable. We also show that minimality and Poincar\'e recurrence are both expressible in the language of ${\sf ITL^c}$, thus providing a decidable logic expressive enough to reason about non-trivial asymptotic behavior in dynamical systems

Operational asset replacement strategy : a real options approach

This article analyses the problem of replacement by investigating the optimal moment of investment replacement in a given tax environment with a given depreciation policy. An operation and maintenance cost minimization model, based on the definition of equivalent annual cost, is applied to a real options paradigm. The developed methodology allows for an innovative evaluation of the flexibility of replacement process analysis. A new two- factor evaluation function is introduced to quantify decisions of asset replacement under a unique cycle environment. This study improves upon previous findings in the literature as it accounts for autonomous salvage value processes. Based on partial differential equations, this model achieves a general analytical solution and particular numerical solution. The results differ significantly from those observed in one-factor models by showing evidence of over-evaluation in optimal levels of replacement, and by confirming suspicions that different types of uncertainties produce non-monotonous effects on the optimal replacement level. The scientific contribution of this study lies in new and stronger approaches to equivalent annual cost literature, supplying an algorithm for operation and maintenance cost minimization that is conditioned by autonomous salvage value. This study also contributes to the real options literature by developing of a two-factor model with Brownian processes applied to asset replacement.info:eu-repo/semantics/publishedVersio

Exact results and mean field approximation for a model of molecular aggregation

We present a simple one-dimensional model with molecular interactions favouring the formation of clusters with a defined optimal size. Increasing the density, at low temperature, the system goes from a nearly-ideal gas of independent molecules to a system with most of the molecules in optimal clusters, in a way that resembles the formation of micelles in a dilution of amphiphilic molecules, at the critical micellar concentration. Our model is simple enough to have an exact solution, but it contains some basic features of more realistic descriptions of amphiphilic systems: molecular excluded volume and molecular attractions which are saturated at the optimal cluster. The comparison between the exact results and the mean field density functional approximation suggests new approaches to study the more complex and realistic models of micelle formation; in particular it addresses the long-standing controversy surrounding separation of internal degrees of freedom in the formulation of cluster association phenomena.Comment: 7 pages, 5 figures, some minor correction

Succinctness in subsystems of the spatial mu-calculus

In this paper we systematically explore questions of succinctness in modal logics employed in spatial reasoning. We show that the closure operator, despite being less expressive, is exponentially more succinct than the limit-point operator, and that the $\mu$-calculus is exponentially more succinct than the equally-expressive tangled limit operator. These results hold for any class of spaces containing at least one crowded metric space or containing all spaces based on ordinals below $\omega^\omega$, with the usual limit operator. We also show that these results continue to hold even if we enrich the less succinct language with the universal modality

Comment on "Spin-1 aggregation model in one dimension"

M. Girardi and W. Figueiredo have proposed a simple model of aggregation in one dimension to mimic the self-assembly of amphiphiles in aqueous solution [Phys. Rev. E 62, 8344 (2000)]. We point out that interesting results can be obtained if a different set of interactions is considered, instead of their choice (the s=1 Ising model).Comment: Accepted for publication in Phys. Rev.