The Shadows of a Cycle Cannot All Be Paths

A "shadow" of a subset $S$ of Euclidean space is an orthogonal projection of $S$ into one of the coordinate hyperplanes. In this paper we show that it is not possible for all three shadows of a cycle (i.e., a simple closed curve) in $\mathbb R^3$ to be paths (i.e., simple open curves). We also show two contrasting results: the three shadows of a path in $\mathbb R^3$ can all be cycles (although not all convex) and, for every $d\geq 1$, there exists a $d$-sphere embedded in $\mathbb R^{d+2}$ whose $d+2$ shadows have no holes (i.e., they deformation-retract onto a point).Comment: 6 pages, 10 figure

Robots with Lights: Overcoming Obstructed Visibility Without Colliding

Robots with lights is a model of autonomous mobile computational entities operating in the plane in Look-Compute-Move cycles: each agent has an externally visible light which can assume colors from a fixed set; the lights are persistent (i.e., the color is not erased at the end of a cycle), but otherwise the agents are oblivious. The investigation of computability in this model, initially suggested by Peleg, is under way, and several results have been recently established. In these investigations, however, an agent is assumed to be capable to see through another agent. In this paper we start the study of computing when visibility is obstructable, and investigate the most basic problem for this setting, Complete Visibility: The agents must reach within finite time a configuration where they can all see each other and terminate. We do not make any assumption on a-priori knowledge of the number of agents, on rigidity of movements nor on chirality. The local coordinate system of an agent may change at each activation. Also, by definition of lights, an agent can communicate and remember only a constant number of bits in each cycle. In spite of these weak conditions, we prove that Complete Visibility is always solvable, even in the asynchronous setting, without collisions and using a small constant number of colors. The proof is constructive. We also show how to extend our protocol for Complete Visibility so that, with the same number of colors, the agents solve the (non-uniform) Circle Formation problem with obstructed visibility

Shape formation by programmable particles

Shape formation (or pattern formation) is a basic distributed problem for systems of computational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter, where entities are assumed to be small and with severely limited capabilities. Namely, it has been studied in the geometric Amoebot model, where the anonymous entities, called particles, operate on a hexagonal tessellation of the plane and have limited computational power (they have constant memory), strictly local interaction and communication capabilities (only with particles in neighboring nodes of the grid), and limited motorial capabilities (from a grid node to an empty neighboring node); their activation is controlled by an adversarial scheduler. Recent investigations have shown how, starting from a well-structured configuration in which the particles form a (not necessarily complete) triangle, the particles can form a large class of shapes. This result has been established under several assumptions: agreement on the clockwise direction (i.e., chirality), a sequential activation schedule, and randomization (i.e., particles can flip coins to elect a leader). In this paper we provide a characterization of which shapes can be formed deterministically starting from any simply connected initial configuration of n particles. The characterization is constructive: we provide a universal shape formation algorithm that, for each feasible pair of shapes (S0, SF), allows the particles to form the final shape SF (given in input) starting from the initial shape S0, unknown to the particles. The final configuration will be an appropriate scaled-up copy of SF depending on n. If randomization is allowed, then any input shape can be formed from any initial (simply connected) shape by our algorithm, provided that there are enough particles. Our algorithm works without chirality, proving that chirality is computationally irrelevant for shape formation. Furthermore, it works under a strong adversarial scheduler, not necessarily sequential. We also consider the complexity of shape formation both in terms of the number of rounds and the total number of moves performed by the particles executing a universal shape formation algorithm. We prove that our solution has a complexity of O(n2) rounds and moves: this number of moves is also asymptotically worst-case optimal

Mutual visibility by luminous robots without collisions

We consider the Mutual Visibility problem for anonymous dimensionless robots with obstructed visibility moving in a plane: starting from distinct locations, the robots must reach, without colliding, a configuration where no three of them are collinear. We study this problem in the luminous robots model, in which each robot has a visible light that can assume colors from a fixed set. Among other results, we prove that Mutual Visibility can be solved in SSynch with 2 colors and in ASynch with 3 colors. If an adversary can interrupt and stop a robot moving to its computed destination, Mutual Visibility is still solvable in SSynch with 3 colors and, if the robots agree on the direction of one axis, also in ASynch. As a byproduct, we provide the first obstructed-visibility solutions to two classical problems for oblivious robots: collision-less convergence to a point (also known as near-gathering) and circle formation

Population protocols with faulty interactions: The impact of a leader

We consider the problem of simulating traditional popula-tion protocols under weaker models of communication, which include one-way interactions (as opposed to two-way interactions) and omission faults (i.e., failure by an agent to read its partner’s state during an inter-action), which in turn may be detectable or undetectable. We focus on the impact of a leader, and we give a complete characterization of the models in which the presence of a unique leader in the system allows the construction of simulators: when simulations are possible, we give explicit protocols; when they are not, we give proofs of impossibility. Specifically, if each agent has only a finite amount of memory, the simulation is pos-sible only if there are no omission faults. If agents have an unbounded amount of memory, the simulation is possible as long as omissions are detectable. If an upper bound on the number of omissions involving the leader is known, the simulation is always possible, except in the one-way model in which one side is unable to detect the interaction

Oblivious permutations on the plane

We consider a distributed system of n identical mobile robots operating in the two dimensional Euclidian plane. As in the previous studies, we consider the robots to be anonymous, oblivious, dis-oriented, and without any communication capabilities, operating based on the Look-Compute-Move model where the next location of a robot depends only on its view of the current configuration. Even in this seemingly weak model, most formation problems which require constructing specific configurations, can be solved quite easily when the robots are fully synchronized with each other. In this paper we introduce and study a new class of problems which, unlike the studied formation problems, cannot always be solved even in the fully synchronous model with atomic and rigid moves. This class of problems requires the robots to permute their locations in the plane. In particular, we are interested in implementing two special types of permutations - permutations without any fixed points and permutations of order n. The former (called Move-All) requires each robot to visit at least two of the initial locations, while the latter (called Visit-All) requires every robot to visit each of the initial locations in a periodic manner. We provide a characterization of the solvability of these problems, showing the main challenges in solving this class of problems for mobile robots. We also provide algorithms for the feasible cases, in particular distinguishing between one-step algorithms (where each configuration must be a permutation of the original configuration) an

Characterisation of the Immunophenotype of Dogs with Primary Immune-Mediated Haemolytic Anaemia

Immune-mediated haemolytic anaemia (IMHA) is reported to be the most common autoimmune disease of dogs, resulting in significant morbidity and mortality in affected animals. Haemolysis is caused by the action of autoantibodies, but the immunological changes that result in their production have not been elucidated.To investigate the frequency of regulatory T cells (Tregs) and other lymphocyte subsets and to measure serum concentrations of cytokines and peripheral blood mononuclear cell expression of cytokine genes in dogs with IMHA, healthy dogs and dogs with inflammatory diseases.19 dogs with primary IMHA, 22 dogs with inflammatory diseases and 32 healthy control dogs.Residual EDTA-anti-coagulated blood samples were stained with fluorophore-conjugated monoclonal antibodies and analysed by flow cytometry to identify Tregs and other lymphocyte subsets. Total RNA was also extracted from peripheral blood mononuclear cells to investigate cytokine gene expression, and concentrations of serum cytokines (interleukins 2, 6 10, CXCL-8 and tumour necrosis factor α) were measured using enhanced chemiluminescent assays. Principal component analysis was used to investigate latent variables that might explain variability in the entire dataset.There was no difference in the frequency or absolute numbers of Tregs among groups, nor in the proportions of other lymphocyte subsets. The concentrations of pro-inflammatory cytokines were greater in dogs with IMHA compared to healthy controls, but the concentration of IL-10 and the expression of cytokine genes did not differ between groups. Principal component analysis identified four components that explained the majority of the variability in the dataset, which seemed to correspond to different aspects of the immune response.The immunophenotype of dogs with IMHA differed from that of dogs with inflammatory diseases and from healthy control dogs; some of these changes could suggest abnormalities in peripheral tolerance that permit development of autoimmune disease. The frequency of Tregs did not differ between groups, suggesting that deficiency in the number of these cells is not responsible for development of IMHA

Asynchronous rendezvous with different maps

© Springer Nature Switzerland AG 2019. This paper provides a study on the rendezvous problem in which two anonymous mobile entities referred to as robots rA and rB are asked to meet at an arbitrary node of a graph G = (V,E). As opposed to more standard assumptions robots may not be able to visit the entire graph G. Namely, each robot has its own map which is a connected subgraph of G. Such mobility restrictions may be dictated by the topological properties combined with the intrinsic characteristics of robots preventing them from visiting certain edges in E. We consider four different variants of the rendezvous problem introduced in [Farrugia et al. SOFSEM’15] which reflect on restricted maneuverability and navigation ability of rA and rB in G. In the latter, the focus is on models in which robots’ actions are synchronised. The authors prove that one of the maps must be a subgraph of the other. I.e., without this assumption (or some extra knowledge) the rendezvous problem does not have a feasible solution. In this paper, while we keep the containment assumption, we focus on asynchronous robots and the relevant bounds in the four considered variants. We provide some impossibility results and almost tight lower and upper bounds when the solutions are possible