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

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

Secure aggregation of distributed information: How a team of agents can safely share secrets in front of a spy

We consider the generic problem of Secure Aggregation of Distributed Information (SADI), where several agents acting as a team have information distributed among them, modeled by means of a publicly known deck of cards distributed among the agents, so that each of them knows only her cards. The agents have to exchange and aggregate the information about how the cards are distributed among them by means of public announcements over insecure communication channels, intercepted by an adversary "eavesdropper", in such a way that the adversary does not learn who holds any of the cards. We present a combinatorial construction of protocols that provides a direct solution of a class of SADI problems and develop a technique of iterated reduction of SADI problems to smaller ones which are eventually solvable directly. We show that our methods provide a solution to a large class of SADI problems, including all SADI problems with sufficiently large size and sufficiently balanced card distributions

Well-orders in the transfinite Japaridze algebra

This paper studies the transfinite propositional provability logics \glp_\Lambda and their corresponding algebras. These logics have for each ordinal $\xi< \Lambda$ a modality \la \alpha \ra. We will focus on the closed fragment of \glp_\Lambda (i.e., where no propositional variables occur) and \emph{worms} therein. Worms are iterated consistency expressions of the form \la \xi_n\ra \ldots \la \xi_1 \ra \top. Beklemishev has defined well-orderings $<_\xi$ on worms whose modalities are all at least $\xi$ and presented a calculus to compute the respective order-types. In the current paper we present a generalization of the original $<_\xi$ orderings and provide a calculus for the corresponding generalized order-types $o_\xi$. Our calculus is based on so-called {\em hyperations} which are transfinite iterations of normal functions. Finally, we give two different characterizations of those sequences of ordinals which are of the form \la {\formerOmega}_\xi (A) \ra_{\xi \in \ord} for some worm $A$. One of these characterizations is in terms of a second kind of transfinite iteration called {\em cohyperation.}Comment: Corrected a minor but confusing omission in the relation between Veblen progressions and hyperation

Hyperations, Veblen progressions and transfinite iterations of ordinal functions

In this paper we introduce hyperations and cohyperations, which are forms of transfinite iteration of ordinal functions. Hyperations are iterations of normal functions. Unlike iteration by pointwise convergence, hyperation preserves normality. The hyperation of a normal function f is a sequence of normal functions so that f^0= id, f^1 = f and for all ordinals \alpha, \beta we have that f^(\alpha + \beta) = f^\alpha f^\beta. These conditions do not determine f^\alpha uniquely; in addition, we require that the functions be minimal in an appropriate sense. We study hyperations systematically and show that they are a natural refinement of Veblen progressions. Next, we define cohyperations, very similar to hyperations except that they are left-additive: given \alpha, \beta, f^(\alpha + \beta)= f^\beta f^\alpha. Cohyperations iterate initial functions which are functions that map initial segments to initial segments. We systematically study cohyperations and see how they can be employed to define left inverses to hyperations. Hyperations provide an alternative presentation of Veblen progressions and can be useful where a more fine-grained analysis of such sequences is called for. They are very amenable to algebraic manipulation and hence are convenient to work with. Cohyperations, meanwhile, give a novel way to describe slowly increasing functions as often appear, for example, in proof theory

The Evolution of Primate Societies - Chapter 3

Compared with other primates, New World monkeys display relatively limited ecological variability. New World monkey anatomy and social systems, however, are extremely diverse. Several unique morphological features (e.g., claws, prehensile tails) and uncommon patterns of social organization (e.g., paternal care, cooperative breeding, female dispersal) have evolved in some platyrrhine species. Social organization and mating patterns include typical harem- like structures where mating is largely polygynous, and large multimale, multifemale groups with promiscuous mating and fi ssion- fusion societies. In addition, some species are socially monogamous and polyandrous. Even closely related species may exhibit strikingly different social organizations, as the example of the squirrel monkeys demonstrates (Mitchell et al. 1991; Boinski et al. 2005b). New World monkey behavior varies within species as well as between them. While the behavior of many species is known from only one study site, intriguing patterns of intraspecific variation are beginning to emerge from observations of populations that sometimes live in close proximity. For example, spider monkeys are often described as showing sex- segregated ranging behavior. Several studies show that males range farther, travel faster, and use larger areas than females, who tend to restrict their habitual ranging to smaller core areas within a group’s large territory (Symington 1988; Chapman 1990; Shimooka 2005). In at least one well- studied population in Yasuní National Park, Ecuador, however, males and females both travel over the entire community home range, and different females within the community show little evidence of occupying distinct core areas (Spehar et al. 2010). Similarly, in most well- studied populations of spider monkeys, females disperse and the resident males within a group are presumed to be close relatives—a suggestion corroborated by genetic data for one local population of spider monkeys in Yasuní. Still, in a different local population, males are not closely related to one another, an unexpected pattern if signifi cant male philopatry were common (Di Fiore 2009; Di Fiore et al. 2009). While the causes of this local variation in group genetic structure are not clear, it may be signifi cant that the groups examined likely had different histories of contact with humans. For longlived animals who occupy relatively small social groups, the loss of even a handful of individuals to hunting, or to any other demographic disturbance, can have a dramatic impact on a group’s genetic structure. Intragroup social relationships, in turn, are likely to be infl uenced by patterns of intragroup relatedness and by the relative availability of social partners of different age or sex class (chapter 21, this volume). Thus, historical and demographic contingencies are likely to create conditions where considerable local, intrapopulation variation in social systems exists. Slight changes in ecological conditions may also contribute to variation in the behavior of individuals living in a single population over time. For example, some authors have hypothesized that howler monkey populations may undergo dramatic fluctuations in size and composition in response to several ecological factors, including resource abundance, parasite and predation pressure, and climate (Milton 1982; Crockett & Eisenberg 1986; Crockett 1996; Milton 1996; Rudran & Fernandez- Duque 2003). This variability, not only among populations, but also within populations across time highlights the need for long- term studies. In sum, our understanding of the behavior of New World monkeys has increased dramatically over the past 25 years. This understanding highlights how their behavior varies within populations over time and among populations or species across space. As our knowledge of platyrrhine behavior continues to unfold and is enriched via additional long- term studies, a central challenge will be to explain how these variations arise. It will be important to entertain adaptive explanations while acknowledging that some differences may emerge via stochastic changes in demography (Struhsaker 2008) or nongenetic, relatively short- term, nonadaptive responses to sudden ecological change

Evidence and plausibility in neighborhood structures

The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a neighborhood semantics, where a neighborhood $N$ indicates that the agent has reason to believe that the true state of the world lies in $N$. Further notions of relative plausibility between worlds and beliefs based on the latter ordering are then defined in terms of this evidence structure, yielding our intended models for evidence-based beliefs. In addition, we also consider a second more general flavor, where belief and plausibility are modeled using additional primitive relations, and we prove a representation theorem showing that each such general model is a $p$-morphic image of an intended one. This semantics invites a number of natural special cases, depending on how uniform we make the evidence sets, and how coherent their total structure. We give a structural study of the resulting `uniform' and `flat' models. Our main result are sound and complete axiomatizations for the logics of all four major model classes with respect to the modal language of evidence, belief and safe belief. We conclude with an outlook toward logics for the dynamics of changing evidence, and the resulting language extensions and connections with logics of plausibility change