Ferdinand Peper

Response to Comment on `Zero and negative energy dissipation at information-theoretic erasure'

We prove that statistical information-theoretic quantities, such as information entropy, cannot generally be interrelated with the lower limit of energy dissipation during information erasure. We also point out that, in deterministic and error-free computers, the information entropy of memories does not change during erasure because its value is always zero. On the other hand, for information-theoretic erasure—i.e., “thermalization”/randomization of the memory—the originally zero information entropy (with deterministic data in the memory) changes after erasure to its maximum value, 1 bit/memory bit, while the energy dissipation is still positive, even at parameters for which the thermodynamic entropy within the memory cell does not change. Information entropy does not convert to thermodynamic entropy and to the related energy dissipation; they are quantities of different physical nature. Possible specific observations (if any) indicating convertibility are at most fortuitous and due to the disregard of additional processes that are present.

Turing-Completeness of Asynchronous Non-camouflage Cellular Automata

Asynchronous Boolean totalistic cellular automata have recently attracted attention as promising models for the implementation of reaction-diffusion systems. It is unknown, however, to what extent they are able to conduct computation. In this paper, we introduce the so-called non-camouflage property, which means that a cell’s update is insensitive to neighboring states that equal its own state. This property is stronger than the Boolean totalistic property, which signifies the existence of states in a cell’s neighborhood, but is not concerned with how many cells are in those states. We argue that the non-camouflage property is extremely useful for the implementation of reaction-diffusion systems, and we construct an asynchronous cellular automaton with this property that is Turing-complete. This indicates the feasibility of computation by reaction-diffusion systems.

Pattern Formation and Computation by Autonomous Chemical Reaction Diffusion Model Inspired by Cellular Automata

We introduce two autonomous chemical reaction-diffusion models that can emulate the behavior of specific cellular automata. One model conducts formation of a 3-color checker-board pattern using an abstract chemical reaction network. The other model is based on a DNA reaction-diffusion system that is capable of emulating a Turing-complete one-dimensional cellular automaton. These frameworks can be used to systematically program spatiotemporal pattern formation, and thus has a potential for an effective macro-scale control of molecular systems.

On a Universal Brownian Cellular Automata with 3 States and 2 Rules

This paper presents a 3-state asynchronous CA that requires merely two transition rules to achieve computational universality. This universality is achieved by embedding Priese’s delay-insensitive circuit elements, called the E-element and the K-element, on the cell space of a so-called Brownian CA, which is an asynchronous CA containing local configurations that conduct a random walk in the circuit topology.

On Neuro-inspired Wireless Sensor Networks

The complexity of nodes in wireless sensor networks is an important variable that determines their size, cost, and functionality. When these factors are drastically minimized, new applications become possible in which nodes are not only truly ubiquitous in the environment, but also available in huge numbers. This article discusses concepts from neuroscience that will be useful in the miniaturization of nodes as well as in the optimization of the sensing and communication strategies employed.

Information, noise and energy dissipation : Laws, limits and applications

This chapter addresses various subjects, including some open questions related to energy dissipation, information, and noise, that are relevant for nano- and molecular electronics. The object is to give a brief and coherent presentation of the results of a number of recent studies of ours.

An Asynchronous Updating Scheme for a Cellular Logic Memory Array

The Cellular Logic Memory Array (CLMA) is a parallel computing paradigm based on an array of memory elements. Each of the memory elements can be configured as a binary logic element or a piece of wiring depending on the contents written in the element. Together these memory elements form a logic circuit that is able to conduct logic operations by sending signals along the elements. The CLMA is originally designed as a synchronous system with clock signals, but it should be operated without clock signals to achieve low-power consumption and efficient computation. As a first step towards an asynchronous CLMA, we present an asynchronous updating scheme in CLMA. Binary signals in the original CLMA are extended to eight-level signals that contain temporal information, so that the resulting functions of logic and wiring resemble that of a synchronously timed scheme. We show that the presented CLMA can operate the same function as in the original CLMA, though some overhead is sustained.

Average consensus in asymmetric broadcasting wireless sensor networks through gossiping

Average consensus algorithms have attracted increasing interest in the last decade because of their potential for use in high-density wireless sensor networks. This paper analyzes an algorithm that is based on a model of asymmetric broadcasting on a random geometric graph, in which nodes broadcast and listen only intermittently. We show that each node can easily estimate its update weight from the degree of silence in its neighborhood, and, after the weights have been assigned in this way, that the consensus algorithm converges to the true average. Both a synchronous and an asynchronous update model are analyzed.

Reconfiguration in Defect-Tolerant Asynchronous Cellular Automata

Defect-tolerance, the ability to overcome unreliability of components in a system, will be essential to realize computers built by nanotechnology, so-called nanocomputers. This paper presents a novel approach to defect-tolerance for nanocomputers that are based on self-timed cellular automata, a type of asynchronous cellular automaton. According to this approach, defective cells are detected and isolated by a wrapping layer. Circuit modules that are used for conducting computation are then placed on the non-defective regions of cell space. We show that communications between modules can be correctly established by introducing a Bus line configuration.

Extracting Transition Rules from a 3-Dimensional Cellular Automaton Representing fMRI Data of a Visual Stimulus Experiment

Functional magnetic resonance imaging (fMRI) is a technique to measure brain activity dynamics as the time series of spatial measurement units (voxels). Each voxel aggregates the neural activity in its spatial region, which changes over time depending on an external stimulus and the activities of other voxels. This paper uses fMRI data from a visual stimulus experiment to extract transition rules in a cellular automaton-like formulation. We identify states in the brain through k-means clustering and determine basic transition rules from the sequences of states. The relevant voxels in each rule are selected based on their statistical characteristics, resulting in a compact formulation of rewriting rules.