On probabilistic analog automata

We consider probabilistic automata on a general state space and study their computational power. The model is based on the concept of language recognition by probabilistic automata due to Rabin and models of analog computation in a noisy environment suggested by Maass and Orponen, and Maass and Sontag. Our main result is a generalization of Rabin's reduction theorem that implies that under very mild conditions, the computational power of the automaton is limited to regular languages

Multiorder neurons for evolutionary higher-order clustering and growth

This letter proposes to use multiorder neurons for clustering irregularly shaped data arrangements. Multiorder neurons are an evolutionary extension of the use of higher-order neurons in clustering. Higher-order neurons parametrically model complex neuron shapes by replacing the classic synaptic weight by higher-order tensors. The multiorder neuron goes one step further and eliminates two problems associated with higher-order neurons. First, it uses evolutionary algorithms to select the best neuron order for a given problem. Second, it obtains more information about the underlying data distribution by identifying the correct order for a given cluster of patterns. Empirically we observed that when the correlation of clusters found with ground truth information is used in measuring clustering accuracy, the proposed evolutionary multiorder neurons method can be shown to outperform other related clustering methods. The simulation results from the Iris, Wine, and Glass data sets show significant improvement when compared to the results obtained using self-organizing maps and higher-order neurons. The letter also proposes an intuitive model by which multiorder neurons can be grown, thereby determining the number of clusters in data

Decoding co-/post-transcriptional complexities of plant transcriptomes and epitranscriptome using next-generation sequencing technologies

Next-generation sequencing (NGS) technologies – Illumina RNA-seq, Pacific Biosciences isoform sequencing (PacBio Iso-seq), and Oxford Nanopore direct RNA sequencing (DRS) - have revealed the complexity of plant transcriptomes and their regulation at the co-/posttranscriptional level. Global analysis of mature mRNAs, transcripts from nuclear run-on assays, and nascent chromatin-bound mRNAs using short as well as full-length and single-molecule DRS reads have uncovered potential roles of different forms of RNA polymerase II during the transcription process, and the extent of co-transcriptional pre-mRNA splicing and polyadenylation. These tools have also allowed mapping of transcriptome-wide start sites in cap-containing RNAs, poly(A) site choice, poly(A) tail length, and RNA base modifications. Analysis of a large number of plant transcriptomes using high-throughput short and long reads under different conditions has established that diverse abiotic and biotic stresses and environmental cues such as light, which regulates many aspects of plant growth and development, have a profound impact on gene expression at the co-/post-transcriptional level. The emerging theme from these studies is that reprogramming of gene expression in response to developmental cues and stresses at the co-/post transcriptional level likely plays a crucial role in eliciting appropriate responses for optimal growth and plant survival under adverse conditions. Although the mechanisms by which developmental cues and different stresses regulate co-/posttranscriptional splicing are largely unknown, a few recent studies are beginning to provide some insights into these mechanisms. These studies indicate that the external cues target spliceosomal and splicing regulatory proteins to modulate alternative splicing. In this review, we provide an overview of recent discoveries on the dynamics and complexities of plant transcriptomes, mechanistic insights into splicing regulation, and discuss critical gaps in co-/post-transcriptional research that need to be addressed using diverse genomic and biochemical approaches

Turing machines can be efficiently simulated by the General Purpose Analog Computer

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity level, by showing that, modulo polynomial reductions, computations of Turing machines can be simulated by GPACs, without the need of using more (space) resources than those used in the original Turing computation, as long as we are talking about bounded computations. In other words, computations done by the GPAC are as space-efficient as computations done in the context of Computable Analysis

An Interface View of Directed Sandpile Dynamics

We present a directed unloading sand box type avalanche model, driven by slowly lowering the retaining wall at the bottom of the slope. The avalanche propagation in the two dimensional surface is related to the space-time configurations of one dimensional Kardar-Parisi-Zhang (KPZ) type interface growth dynamics. We express the scaling exponents for the avalanche cluster distributions into that framework. The numerical results agree closely with KPZ scaling, but not perfectly.Comment: 4 pages including 5 figure

A Description of the Agriculture and Type-of-Farming Areas in Texas.

91 p

Energy constrained sandpile models

We study two driven dynamical systems with conserved energy. The two automata contain the basic dynamical rules of the Bak, Tang and Wiesenfeld sandpile model. In addition a global constraint on the energy contained in the lattice is imposed. In the limit of an infinitely slow driving of the system, the conserved energy $E$ becomes the only parameter governing the dynamical behavior of the system. Both models show scale free behavior at a critical value $E_c$ of the fixed energy. The scaling with respect to the relevant scaling field points out that the developing of critical correlations is in a different universality class than self-organized critical sandpiles. Despite this difference, the activity (avalanche) probability distributions appear to coincide with the one of the standard self-organized critical sandpile.Comment: 4 pages including 3 figure

Dynamically Driven Renormalization Group Applied to Sandpile Models

The general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the Dynamically Driven Renormalization Group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.Comment: 18 RevTeX pages, 5 figure