Combinatorial Solutions Providing Improved Security for the Generalized Russian Cards Problem

We present the first formal mathematical presentation of the generalized Russian cards problem, and provide rigorous security definitions that capture both basic and extended versions of weak and perfect security notions. In the generalized Russian cards problem, three players, Alice, Bob, and Cathy, are dealt a deck of $n$ cards, each given $a$, $b$, and $c$ cards, respectively. The goal is for Alice and Bob to learn each other's hands via public communication, without Cathy learning the fate of any particular card. The basic idea is that Alice announces a set of possible hands she might hold, and Bob, using knowledge of his own hand, should be able to learn Alice's cards from this announcement, but Cathy should not. Using a combinatorial approach, we are able to give a nice characterization of informative strategies (i.e., strategies allowing Bob to learn Alice's hand), having optimal communication complexity, namely the set of possible hands Alice announces must be equivalent to a large set of $t-(n, a, 1)$-designs, where $t=a-c$. We also provide some interesting necessary conditions for certain types of deals to be simultaneously informative and secure. That is, for deals satisfying $c = a-d$ for some $d \geq 2$, where $b \geq d-1$ and the strategy is assumed to satisfy a strong version of security (namely perfect $(d-1)$-security), we show that $a = d+1$ and hence $c=1$. We also give a precise characterization of informative and perfectly $(d-1)$-secure deals of the form $(d+1, b, 1)$ satisfying $b \geq d-1$ involving $d-(n, d+1, 1)$-designs

The KIT swiss knife gripper for disassembly tasks: a multi-functional gripper for bimanual manipulation with a single arm

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This work presents the concept of a robotic gripper designed for the disassembly of electromechanical devices that comprises several innovative ideas. Novel concepts include the ability to interchange built-in tools without the need to grasp them, the ability to reposition grasped objects in-hand, the capability of performing classic dual arm manipulation within the gripper and the utilization of classic industrial robotic arms kinematics within a robotic gripper. We analyze state of the art grippers and robotic hands designed for dexterous in-hand manipulation and extract common characteristics and weak points. The presented concept is obtained from the task requirements for disassembly of electromechanical devices and it is then evaluated for general purpose grasping, in-hand manipulation and operations with tools. We further present the CAD design for a first prototype.Peer ReviewedPostprint (author's final draft

Exploring Young Students' Functional Thinking

The Early Years Generalising Project (EYGP) involves Australian Years 1-4 (age 5-9) students and investigates how they grasp and express generalisations. This paper focuses on data collected from six Year 1 students in an exploratory study within a clinical interview setting that required students to identify function rules. Preliminary findings suggest that the use of gestures (both by students and interviewers), self-talk (by students), and concrete acting out, assisted students to reach generalisations and to begin to express these generalities. It also appears that as students become aware of the structure, their use of gestures and self- talk tended to decrease

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

Layers of generality and types of generalization in pattern activities

Pattern generalization is considered one of the prominent routes for in-troducing students to algebra. However, not all generalizations are al-gebraic. In the use of pattern generalization as a route to algebra, we —teachers and educators— thus have to remain vigilant in order not to confound algebraic generalizations with other forms of dealing with the general. But how to distinguish between algebraic and non-algebraic generalizations? On epistemological and semiotic grounds, in this arti-cle I suggest a characterization of algebraic generalizations. This char-acterization helps to bring about a typology of algebraic and arithmetic generalizations. The typology is illustrated with classroom examples

Splitting hairs with transcendental entire functions

For polynomials of degree at least two, local connectivity of their Julia set is an important property, since it leads to a complete description of their topological dynamics in terms of a simpler model. There is no such connection between the topology of the Julia set of a transcendental entire function $f$ and its dynamics. Nonetheless, it has been shown that one can still describe the dynamics of $f$ in terms of a simpler model, assuming that its \textit{postsingular set} is bounded and $f$ satisfies certain additional hyperbolicity assumptions. Our goal in this paper is, for the first time, to give analogous results in cases when the postsingular set is unbounded. More specifically, we show that if $f$ is of finite order, has \textit{bounded criticality} on its Julia set, and its singular set consists of finitely many critical values that escape to infinity and satisfy a certain separation condition, then its Julia set $J(f)$ is a collection of \textit{dynamic rays} or \emph{hairs}, that \emph{split} at (preimages of) critical points, together with their corresponding landing points. In fact, our result holds for a much larger class of functions; in particular, the assumption of finite order is relaxed to the existence of a map in their parameter space whose Julia set is a \textit{Cantor bouquet}. The existence and landing of rays is a consequence of a more general result; we provide a \textit{topological model} for the action of $f$ on $J(f)$. Finally, we present new results concerning \textit{disjoint type} functions in the case that the Julia set is a Cantor bouquet.Comment: 69 pages, 8 figure

An epistemic dimension space for musical devices

The analysis of digital music systems has traditionally been characterized by an approach that can be defined as phenomenological. The focus has been on the body and its relationship to the machine, often neglecting the system’s conceptual design. This paper brings into focus the epistemic features of digital systems, which implies emphasizing the cognitive, conceptual and music theoretical side of our musical instruments. An epistemic dimension space for the analysis of musical devices is proposed