A Local Stochastic Algorithm for Separation in Heterogeneous Self-Organizing Particle Systems

We present and rigorously analyze the behavior of a distributed, stochastic algorithm for separation and integration in self-organizing particle systems, an abstraction of programmable matter. Such systems are composed of individual computational particles with limited memory, strictly local communication abilities, and modest computational power. We consider heterogeneous particle systems of two different colors and prove that these systems can collectively separate into different color classes or integrate, indifferent to color. We accomplish both behaviors with the same fully distributed, local, stochastic algorithm. Achieving separation or integration depends only on a single global parameter determining whether particles prefer to be next to other particles of the same color or not; this parameter is meant to represent external, environmental influences on the particle system. The algorithm is a generalization of a previous distributed, stochastic algorithm for compression (PODC \u2716) that can be viewed as a special case of separation where all particles have the same color. It is significantly more challenging to prove that the desired behavior is achieved in the heterogeneous setting, however, even in the bichromatic case we focus on. This requires combining several new techniques, including the cluster expansion from statistical physics, a new variant of the bridging argument of Miracle, Pascoe and Randall (RANDOM \u2711), the high-temperature expansion of the Ising model, and careful probabilistic arguments

Convex Hull Formation for Programmable Matter

We envision programmable matter as a system of nano-scale agents (called particles) with very limited computational capabilities that move and compute collectively to achieve a desired goal. We use the geometric amoebot model as our computational framework, which assumes particles move on the triangular lattice. Motivated by the problem of sealing an object using minimal resources, we show how a particle system can self-organize to form an object's convex hull. We give a distributed, local algorithm for convex hull formation and prove that it runs in $\mathcal{O}(B)$ asynchronous rounds, where $B$ is the length of the object's boundary. Within the same asymptotic runtime, this algorithm can be extended to also form the object's (weak) $\mathcal{O}$-hull, which uses the same number of particles but minimizes the area enclosed by the hull. Our algorithms are the first to compute convex hulls with distributed entities that have strictly local sensing, constant-size memory, and no shared sense of orientation or coordinates. Ours is also the first distributed approach to computing restricted-orientation convex hulls. This approach involves coordinating particles as distributed memory; thus, as a supporting but independent result, we present and analyze an algorithm for organizing particles with constant-size memory as distributed binary counters that efficiently support increments, decrements, and zero-tests --- even as the particles move

The Canonical Amoebot Model: Algorithms and Concurrency Control

The amoebot model abstracts active programmable matter as a collection of simple computational elements called amoebots that interact locally to collectively achieve tasks of coordination and movement. Since its introduction at SPAA 2014, a growing body of literature has adapted its assumptions for a variety of problems; however, without a standardized hierarchy of assumptions, precise systematic comparison of results under the amoebot model is difficult. We propose the canonical amoebot model, an updated formalization that distinguishes between core model features and families of assumption variants. A key improvement addressed by the canonical amoebot model is concurrency. Much of the existing literature implicitly assumes amoebot actions are isolated and reliable, reducing analysis to the sequential setting where at most one amoebot is active at a time. However, real programmable matter systems are concurrent. The canonical amoebot model formalizes all amoebot communication as message passing, leveraging adversarial activation models of concurrent executions. Under this granular treatment of time, we take two complementary approaches to concurrent algorithm design. We first establish a set of sufficient conditions for algorithm correctness under any concurrent execution, embedding concurrency control directly in algorithm design. We then present a concurrency control framework that uses locks to convert amoebot algorithms that terminate in the sequential setting and satisfy certain conventions into algorithms that exhibit equivalent behavior in the concurrent setting. As a case study, we demonstrate both approaches using a simple algorithm for hexagon formation. Together, the canonical amoebot model and these complementary approaches to concurrent algorithm design open new directions for distributed computing research on programmable matter.Comment: 48 pages, 7 figures, 2 table

Prevalence of hypothyroidism in type 2 diabetic adult Indian females and its correlation with age, HbA1c, BMI and duration of diabetes

Background: Patients with type 2 diabetes mellitus are more prone to thyroid disorders. Hypothyroidism in them leads to an aggravation of microvascular complications. Screening for thyroid dysfunction in diabetic patients will allow early treatment of hypothyroidism. The aim of this study was to assess the prevalence of hypothyroidism in patients with type 2 diabetes mellitus and its correlation with age, HbA1c, BMI and duration of diabetes. Methods: This was a cross sectional study that was conducted at department of medicine GSVM medical college, Kanpur. 200 female patients with type 2 diabetes mellitus attending the outpatient department without any prior history of thyroid disease, chronic liver disease or acute illness were recruited for the study. Results: Our study describes 14% prevalence of hypothyroidism (subclinical hypothyroidism 13.5%) among 200 diabetic subjects. Hypothyroidism was more common in older age group maximum seen in age group 70-79 years (66.7%). Hypothyroidism was more common in subjects having diabetes for a longer duration; maximum seen in 25-30 years group (40%). No correlation was found between BMI and hypothyroidism. Conclusions: The prevalence of hypothyroidism was 14% among female patients with type 2 diabetes mellitus in this study. Overt hypothyroidism was 0.5 % and subclinical hypothyroidism was more common (13.5%) among the study subjects. Hypothyroidism was more common in older age group. and in subjects having diabetes for longer duration. No corelation was found between prevalence of hypothyroidism and body mass index (BMI)

Photoreceptor phosphodiesterase (PDE6): structure, regulatory mechanisms, and implications for treatment of retinal diseases

The photoreceptor phosphodiesterase (PDE6) is a member of large family of Class I phosphodiesterases responsible for hydrolyzing the second messengers cAMP and cGMP. PDE6 consists of two catalytic subunits and two inhibitory subunits that form a tetrameric protein. PDE6 is a peripheral membrane protein that is localized to the signaling-transducing compartment of rod and cone photoreceptors. As the central effector enzyme of the G-protein coupled visual transduction pathway, activation of PDE6 catalysis causes in a rapid decrease in cGMP levels that results in closure of cGMP-gated ion channels in the photoreceptor plasma membrane. Because of its importance in the phototransduction pathway, mutations in PDE6 genes result in various retinal diseases that currently lack therapeutic treatment strategies due to inadequate knowledge of the structure, function, and regulation of this enzyme. This review focuses on recent progress in understanding the structure of the regulatory and catalytic domains of the PDE6 holoenzyme, the central role of the multi-functional inhibitory γ-subunit, the mechanism of activation by the heterotrimeric G protein, transducin, and future directions for pharmacological interventions to treat retinal degenerative diseases arising from mutations in the PDE6 genes

Energy-Constrained Programmable Matter Under Unfair Adversaries

Individual modules of programmable matter participate in their system's collective behavior by expending energy to perform actions. However, not all modules may have access to the external energy source powering the system, necessitating a local and distributed strategy for supplying energy to modules. In this work, we present a general energy distribution framework for the canonical amoebot model of programmable matter that transforms energy-agnostic algorithms into energy-constrained ones with equivalent behavior and an $\mathcal{O}(n^2)$-round runtime overhead -- even under an unfair adversary -- provided the original algorithms satisfy certain conventions. We then prove that existing amoebot algorithms for leader election (ICDCN 2023) and shape formation (Distributed Computing, 2023) are compatible with this framework and show simulations of their energy-constrained counterparts, demonstrating how other unfair algorithms can be generalized to the energy-constrained setting with relatively little effort. Finally, we show that our energy distribution framework can be composed with the concurrency control framework for amoebot algorithms (Distributed Computing, 2023), allowing algorithm designers to focus on the simpler energy-agnostic, sequential setting but gain the general applicability of energy-constrained, asynchronous correctness.Comment: 31 pages, 4 figures, 1 table. Submitted to OPODIS 202