Undecidable Properties of Limit Set Dynamics of Cellular Automata

Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial properties of limit sets are undecidable. In this paper we consider properties of limit set dynamics, i.e. properties of the dynamics of Cellular Automata restricted to their limit sets. There can be no equivalent of Kari's Theorem for limit set dynamics. Anyway we show that there is a large class of undecidable properties of limit set dynamics, namely all properties of limit set dynamics which imply stability or the existence of a unique subshift attractor. As a consequence we have that it is undecidable whether the cellular automaton map restricted to the limit set is the identity, closing, injective, expansive, positively expansive, transitive

Decidable properties for regular cellular automata

We investigate decidable properties for regular cellular automata. In particular, we show that regularity itself is an undecidable property and that nilpotency, equicontinuity and positively expansiveness became decidable if we restrict to regular cellular automata4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

Vital signs monitoring using Ultra Wide Band pulse radar

The aim of this work is to describe how to realize a measurement setup to detect target heart and breath rate with the use of Ultra Wide Band (UWB) radar technology. Thanks to UWB wireless capabilities the detection is done contactless just standing still at a given distance dT. Contactless heart and breath rate detection can be achieved with the use of currently available commercial UWB radar devices. This is of interest for intensive-care patient monitoring, home monitoring, fast disease screening and remote vital signs monitoring. Our setup is composed by devices provided by PulsON: two PulsON 220RD UWB radars. We encountered an issue with time synchronization that is very critical in UWB detection techniques and therefore a custom built synchronization algorithm has been developedope

Performance assessment of capture zones generated by PV-powered pump and treat systems

Pump and treat (P&T) is a technology that has been extensively used to remove and/or contain contaminated groundwater. Hydraulic containment of contaminants is accomplished by generating capture zones through pumping of groundwater. An appropriate delineation of capture zones is necessary to design an effective P&T system. P&T systems conventionally operate continuously to achieve steady-state capture zones, which require significant amounts of energy. The use of renewable energies to meet power demands of remedial systems may reduce a project\u27s carbon dioxide emissions. The hydraulic effectiveness of a photovoltaic (PV) powered P&T system without energy storage was characterized using data collected at two different remediation sites, a Dry-cleaning Environmental Response Trust Fund site in Rolla, Missouri and the Former Nebraska Ordnance Plant near Mead, Nebraska. A method to estimate hydraulic containment effectiveness of PV-powered P&T systems without energy storage was developed. The performance of a hypothetical PV-powered P&T system that operates both intermittently by assuming that the system does not include an energy storage component and continuously by assuming that system includes a relatively small capacity energy storage component was analyzed using widely available Typical Meteorological Year 3 data. A methodology to estimate capture zone widths for PV-powered P&T systems without energy storage throughout the continental U.S. as a function of solar insolation data, transmissivity, and hydraulic gradient was developed. Maps depicting predicted capture zone widths for specified transmissivity values and a hydraulic gradient were developed. The applicability of the developed methodology was illustrated with two actual sites where groundwater remediation has taken place. --Abstract, page iv

Correlation Plenoptic Imaging With Entangled Photons

Plenoptic imaging is a novel optical technique for three-dimensional imaging in a single shot. It is enabled by the simultaneous measurement of both the location and the propagation direction of light in a given scene. In the standard approach, the maximum spatial and angular resolutions are inversely proportional, and so are the resolution and the maximum achievable depth of focus of the 3D image. We have recently proposed a method to overcome such fundamental limits by combining plenoptic imaging with an intriguing correlation remote-imaging technique: ghost imaging. Here, we theoretically demonstrate that correlation plenoptic imaging can be effectively achieved by exploiting the position-momentum entanglement characterizing spontaneous parametric down-conversion (SPDC) photon pairs. As a proof-of-principle demonstration, we shall show that correlation plenoptic imaging with entangled photons may enable the refocusing of an out-of-focus image at the same depth of focus of a standard plenoptic device, but without sacrificing diffraction-limited image resolution.Comment: 12 pages, 5 figure

Diffraction-limited plenoptic imaging with correlated light

Traditional optical imaging faces an unavoidable trade-off between resolution and depth of field (DOF). To increase resolution, high numerical apertures (NA) are needed, but the associated large angular uncertainty results in a limited range of depths that can be put in sharp focus. Plenoptic imaging was introduced a few years ago to remedy this trade off. To this aim, plenoptic imaging reconstructs the path of light rays from the lens to the sensor. However, the improvement offered by standard plenoptic imaging is practical and not fundamental: the increased DOF leads to a proportional reduction of the resolution well above the diffraction limit imposed by the lens NA. In this paper, we demonstrate that correlation measurements enable pushing plenoptic imaging to its fundamental limits of both resolution and DOF. Namely, we demonstrate to maintain the imaging resolution at the diffraction limit while increasing the depth of field by a factor of 7. Our results represent the theoretical and experimental basis for the effective development of the promising applications of plenoptic imaging.Comment: 10 pages, 10 figure

Global Stability and Plus-Global Stability. An Application to Forward Neural Networks

A necessary and sufficient condition for a discrete dynamical system to be globally stable and plus-globally stable are first established in Section 2. The V-condition is introduced and Theorems 3.5 and 3.7 are presented in Section 3. The two theorems link the V-condition to the most relevant properties of globally stable and plus-globally stable discrete dynamical systems. In Section 4 we provide a simple application to a convergence problem for forward neural networks

Estimage: a webserver hub for the computation of methylation age

Methylage is an epigenetic marker of biological age that exploits the correlation between the methylation state of specific CG dinucleotides (CpGs) and chronological age (in years), gestational age (in weeks), cellular age (in cell cycles or as telomere length, in kilobases). Using DNA methylation data, methylage is measurable via the so called epigenetic clocks. Importantly, alterations of the correlation between methylage and age (age acceleration or deceleration) have been stably associated with pathological states and occur long before clinical signs of diseases become overt, making epigenetic clocks a potentially disruptive tool in preventive, diagnostic and also in forensic applications. Nevertheless, methylage dependency from CpGs selection, mathematical modelling, tissue specificity and age range, still makes the potential of this biomarker limited. In order to enhance model comparisons, interchange, availability, robustness and standardization, we organized a selected set of clocks within a hub webservice, EstimAge (Estimate of methylation Age, http://estimage.iac.rm.cnr.it), which intuitively and informatively enables quick identification, computation and comparison of available clocks, with the support of standard statistics

Editorial: Computational Methods for Analysis of DNA Methylation Data

DNA methylation is among the most studied epigenetic modifications in eukaryotes. The interest in DNA methylation stems from its role in development, as well as its well- established association with phenotypic changes. Particularly, there is strong evidence that methylation pattern alterations in mammals are linked to developmental disorders and cancer (Kulis and Esteller, 2010). Owing to its potential as a prognostic marker for preventive medicine, in recent years, the analysis of DNA methylation data has garnered interest in many different contexts of computational biology (Bock, 2012). As it typically happens with omic data, processing, analyzing and interpreting large-scale DNA methylation datasets requires computational methods and software tools that address multiple challenges. In the present Research Topic, we collected papers that tackle different aspects of computational approaches for the analysis of DNA methylation data. These manuscripts address novel computational solutions for copy number variation detection, cell-type deconvolution and methylation pattern imputation, while others discuss interpretations of well-established computational techniques. Over the last 10 years, DNA methylation profiles have been successfully exploited to develop biomarkers of age, also referred to as epigenetic clocks (Bell et al., 2019). Epigenetic clocks accurately estimate both chronological and biological age from methylation levels. DNA methylation age and, most importantly, its deviation from chronological age have been shown to be associated with a variety of health issues. More recently, a second generation of epigenetic clocks has emerged. The new generation of clocks incorporates not only methylation profiles but also environmental variants, such as smoking and alcohol consumption, and they outperform the first generation in mortality prediction and prognosis of certain diseases. In our collection, the review by Chen et al. compares the first and second generation of epigenetic clocks that predict cancer risk and discusses pathways known to exhibit altered methylation in aging tissues and cancer. Differentially methylated regions (DMRs), that is genomic regions that show significant differences in methylation levels across distinct biological and/or medical conditions (e.g., normal vs. disease), have been reported to be implicated in a variety of disorders (Rakyan et al., 2011). As a result, identifying DMRs is one of the most critical and fundamental challenges in deciphering disease mechanisms at the molecular level. Although DNA methylation patterns remain stable during normal somatic cell growth, alterations in genomic methylation may be caused by genetic alterations, or vice versa. However, standard DMR analysis often ignores whether methylation alterations should be viewed as a cause or an effect. Rhamani et al. discuss the effect of model directionality, i.e. whether the condition of interest (phenotype) may be affected by methylation or whether it may affect methylation, in differential methylation analyses at the cell-type level. They show that correctly accounting for model directionality has a significant impact on the ability to identify cell type specific differential methylation. Different cell types exhibit DMRs at many genomic regions and such rich information can be exploited to infer underlying cell type proportions using deconvolution techniques. DNA methylation-based cell mixture deconvolution approaches can be classified into two main categories: reference-based and reference-free. While the latter are more broadly applicable, as they do not rely on the availability of methylation profiles from each of the purified cell types that compose a tissue of interest, they are also less precise. Reference-based approaches use DMRs specific to cell types (reference library) to determine the underlying cellular composition within a DNA methylation sample. The quality of the reference library has a big impact on the accuracy of reference-based approaches. Bell-Glenn et al. present RESET, a framework for reference library selection for deconvolution algorithms exploiting a modified version of the Dispersion Separability Criteria score, for the inference of the best DMRs composing the library, contributing to de facto standards (Koestler et al., 2016). In short, RESET does not require researchers to identify a priori the size of the reference library (number of DMRs), nor to rely on costly associated purified cells’ mDNA profiles. Within a cellular population, the methylation patterns of different cell types and at specific genomic locations are indicative of cellular heterogeneity. Alterations of such heterogeneity are predictive of development as well as prognostic markers of diseases. Computational methods that exploit heterogeneity in methylation patterns are typically constrained by partially observed patterns due to the nature of shotgun sequencing, which frequently generates limited coverage for downstream analysis. One possible solution to overcome such limitations is offered by Chang et al. presenting BSImp, a probabilistic based imputation method that uses local information to impute partially observed methylation patterns. They show that using this approach they are able to recover heterogeneity estimates at 15% more regions with moderate sequencing depths. This should therefore improve our ability to study how methylation heterogeneity is associated with disease. Finally, recent studies have shown how the associations between Copy Number Variations (CNVs) and methylation alterations offer a richer and hence more informative picture of the samples under study, in particular for tumor data characterized by large scale genomic rearrangements (Sun et al., 2018). Consequently, recent technological and methodological developments have enabled the possibility to measure CNVs from DNA methylation data. The main advantage of DNA methylation based CNV approaches is that they offer the possibility to integrate both genomic (copy number) and epigenomic (methylation) information. Mariani et al. propose MethylMasteR, an R software package that integrates DNA methylation-based CNV calling routines, facilitating standardization, comparison and customization of CNV analyses. This package, built into the Docker architecture to seamlessly mange dependencies, includes four of the most commonly used routines for this integrated analysis, ChAMP (Morris et al., 2014), SeSAMe (Zhou et al., 2018), Epicopy (Cho et al., 2019), plus a custom version of cnAnalysis450k (Knoll et al., 2017), overall enabling analysis of comparative results. All the topics in this issue, although limited to specific aspects of DNA methylation analysis, highlight the importance of research in this field, the associated computational challenges and illustrate the significant impact that this type of data will likely have on preventive medicine