Computable Functions Research Articles

On unstable and unoptimal prediction

AbstractWe consider the notion of prediction functions (or predictors) studied before in the context of randomness and stochasticity by Ko, and later by Ambos‐Spies and others. Predictor is a total computable function which tries to predict bits of some infinite binary sequence. The prediction error is defined as the limit of the number of incorrect answers divided by the number of answers given so far. We discuss indefiniteness of prediction errors for weak 1‐generics and show that this phenomenon affects certain c.e. sequences as well. On the other hand, a notion of optimal predictor is considered. It is shown that there is a sequence for which increasingly better predictors exist but for which no predictor is optimal.

The Gerstenhaber problem for commuting triples of matrices is “decidable”

The Gerstenhaber Problem (GP) asks whether Gerstenhaber’s surprising 1961 theorem for two commuting matrices extends to three commuting n × n matrices A, B, C over a field F: must the (unital) subalgebra of generated by A, B, C have dimension at most n? We show the GP reduces to the prime fields and . Moreover, the GP is “decidable” in terms of Turing computability (a huge reduction in complexity). We also provide some more evidence pointing to a negative answer to the problem.

A biomimetic 2D transistor for audiomorphic computing

In this article, we introduce a biomimetic audiomorphic device that captures the neurobiological architecture and computational map inside the auditory cortex of barn owl known for its exceptional hunting ability in complete darkness using auditory cues. The device consists of multiple split-gates with nanogaps on a semiconducting MoS2 channel connected to the source/drain contacts for imitating the spatial map of coincidence detector neurons and tunable RC circuits for imitating the interaural time delay neurons following the Jeffress model of sound localization. Furthermore, we use global back-gating capability to demonstrate neuroplasticity to capture behavioral and/or adaptation related changes in the barn owl. Finally, the virtual source model for current transport is combined with finite element COMSOL multiphysics simulations to explain and project the performance of the biomimetic audiomorphic device. We find that the precision of the biomimetic device can supersede the barn owl by orders of magnitude.

Exploiting the Intertemporal Structure of the Upper-Limb sEMG: Comparisons between an LSTM Network and Cross-Sectional Myoelectric Pattern Recognition Methods.

The use of natural myoelectric interfaces promises great value for a variety of potential applications, clinical and otherwise, provided a computational mapping between measured neuromuscular activity and executed motion can be approximated to a satisfactory degree. However, prevalent methods intended for such decoding of movement intent from the surface electromyogram (sEMG) based on pattern recognition typically do not capitalize on the inherently time series-like nature of the acquired signals. In this paper, we present the results from a comparative study in which the performances of traditional cross-sectional pattern recognition methods were compared with that of a classifier built on the natural assumption of temporal ordering by utilizing a long short-term memory (LSTM) neural network. The resulting evaluation indicate that the LSTM approach outperforms traditional gesture recognition techniques which are based on cross-sectional inference. These findings held both when the LSTM classifier operated on conventional features and on raw sEMG and for both healthy subjects and transradial amputees.

Interações realizadas por genes líderes do câncer de mama: uma abordagem computacional

Objetivo: Identificar os genes líderes e as interações realizadas por eles na rede do câncer de mama. Métodos: Trata-se de uma pesquisa exploratória de natureza computacional. A identificação dos genes envolvidos com o câncer de mama foi realizada na base de dados de genética humana GeneCards. Para isso, adotou-se o descritor breast cancer, selecionado na biblioteca de descritores de assuntos médicos Medical Subject Headings. Após a identificação dos genes, foi construído um mapa genômico com o auxílio do software Search Tool for the Retrieval of Interacting Genes/Proteins versão 10.0. Resultados: Foram identificados 8.610 genes, sendo selecionados 400 genes com as pontuações mais elevadas para a realização do mapa de interação genômico. Os genes TP53, PIK3CA, AKT1, EGFR, MAPK1, EP300, SRC e CDK2 foram considerados os genes líderes da rede câncer de mama, os quais interagiram com 90, 88, 64, 62, 60, 66, 58 e 52 genes, respectivamente. Interações entre os genes líderes e genes pertencentes a vias moleculares distintas foram realizadas. Conclusão: O mapeamento computacional dos genes mais relevantes para a condição câncer de mama revelou TP53, PIK3CA, AKT1, EGFR, MAPK1, EP300, SRC e CDK2 como genes líderes e as interações realizadas por eles dentro da rede em estudo.

Tailor made biheterocyclic pyrazoline-thiazolidinones as effective inhibitors of Escherichia coli FabH: Design, synthesis and structural studies

In the present study, a new series of biheterocycles pyrazoline-thiazolidinones derivatized at fifth position with substituted arylidene groups were developed as potent inhibitors of Escherichia coli FabH (PDB: 5BNS) an antimicrobial target. These compounds are conveniently synthesized from 3,5-substituted pyrazolinyl carbothioamide precursor. The virtual inhibition assay and pharmacokinetic profiling were carried out based on in vitro antimicrobial assay on pathogenic microbes. Amongst, the compound with 4-methoxy benzylidene substituent emerged as effective against all tested bacterial strains. The compound binds very effectively to the active site of the target with minimum glide score = −8.400 kcal/mol. The structure of newly synthesized derivatives was confirmed by several spectroscopic techniques and some of the hybrids by single crystal XRD studies. The compounds 3, 4a and 4g were crystallized in monoclinic crystal system with P21/c, P21/n and Cc space group respectively. The intermolecular contacts in the crystal structure were elucidated by Hirshfeld computational methods and molecular electrostatic potential maps illustrated the charge distribution of the molecules.

Structure-guided fragment-based drug discovery at the synchrotron: screening binding sites and correlations with hotspot mapping.

Structure-guided drug discovery emerged in the 1970s and 1980s, stimulated by the three-dimensional structures of protein targets that became available, mainly through X-ray crystal structure analysis, assisted by the development of synchrotron radiation sources. Structures of known drugs or inhibitors were used to guide the development of leads. The growth of high-throughput screening during the late 1980s and the early 1990s in the pharmaceutical industry of chemical libraries of hundreds of thousands of compounds of molecular weight of approximately 500 Da was impressive but still explored only a tiny fraction of the chemical space of the predicted 1040 drug-like compounds. The use of fragments with molecular weights less than 300 Da in drug discovery not only decreased the chemical space needing exploration but also increased promiscuity in binding targets. Here we discuss advances in X-ray fragment screening and the challenge of identifying sites where fragments not only bind but can be chemically elaborated while retaining their positions and binding modes. We first describe the analysis of fragment binding using conventional X-ray difference Fourier techniques, with Mycobacterium abscessus SAICAR synthetase (PurC) as an example. We observe that all fragments occupy positions predicted by computational hotspot mapping. We compare this with fragment screening at Diamond Synchrotron Light Source XChem facility using PanDDA software, which identifies many more fragment hits, only some of which bind to the predicted hotspots. Many low occupancy sites identified may not support elaboration to give adequate ligand affinity, although they will likely be useful in drug discovery as ‘warm spots’ for guiding elaboration of fragments bound at hotspots. We discuss implications of these observations for fragment screening at the synchrotron sources.This article is part of the theme issue ‘Fifty years of synchrotron science: achievements and opportunities’.

How Computational Epitope Mapping Identifies the Interactions between Nanoparticles Derived from Papaya Mosaic Virus Capsid Proteins and Immune System.

Background: Nanoparticles derived from plant viruses possess fascinating structures, versa-tile functions and safe properties, rendering them valuable for a variety of applications. Papaya mosaic Virus-Like Particles (VLPs) are nanoparticles that contain a repetitive number of virus capsid proteins (PMV-CP) and are considered to be promising platforms for vaccine design. Previous studies have re-ported the antigenicity of PMV nanoparticles in mammalian systems.Materials and Methods: As experiments that concern vaccine development require careful design and can be time consuming, computational experiments are of particular importance. Therefore, prior to ex-pressing PMV-CP in E. coli and producing nanoparticles, we performed an in silico analysis of the virus particles using software programs based on a series of sophisticated algorithms and modeling networks as useful tools for vaccine design. A computational study of PMV-CP in the context of the immune sys-tem reaction allowed us to clarify particle structure and other unknown features prior to their introduc-tion in vitro.Results: The results illustrated that the produced nanoparticles can trigger an immune response in the absence of fusion with any foreign antigen.Conclusion: Based on the in silico analyses, the empty capsid protein was determined to be recognised by different B and T cells, as well as cells which carry MHC epitopes.

Computational Mapping of the Ground Reflectivity With Laser Scanners.

In this investigation, we focus on the problem of mapping the ground reflectivity with multiple laser scanners mounted on mobile robots/vehicles. The problem originates because regions of the ground become populated with a varying number of reflectivity measurements, whose value depends on the observer and its corresponding perspective. Here, we propose a novel automatic, data-driven computational mapping framework specifically aimed at preserving edge sharpness in the map reconstruction process and that considers the sources of measurement variation. Our new formulation generates map-perspective gradients and applies sub-set selection fusion and de-noising operators to these through iterative algorithms that minimize an l1 sparse regularized least squares formulation. The reconstruction of the ground reflectivity is then carried out based on Poisson's formulation posed as an l2 term promoting consistency with the fused gradient of map-perspectives and a term that ensures equality constraints with reference measurement map data. We demonstrate that our new framework outperforms the capabilities of the existing ones with experiments realized on Ford's fleet of autonomous vehicles. For example, we show that we can achieve map enhancement (i.e., contrast enhancement), artifact removal, de-noising, and map-stitching without requiring an additional reflectivity adjustment to calibrate sensors to the specific mounting and robot/vehicle motion.

Hotspot Identification on Protein Surfaces Using Probe-Based MD Simulations: Successes and Challenges.

Molecular Dynamics (MD) based computational co-solvent mapping methods involve the generation of an ensemble of MD-sampled target protein conformations and using selected small molecule fragments to identify and characterize binding sites on the surface of a target protein. This approach incorporates atomic-level solvation effects and protein mobility. It has shown great promise in the identification of conventional competitive and allosteric binding sites. It is also currently emerging as a useful tool in the early stages of drug discovery. This review summarizes efforts as well as discusses some methodological advances and challenges in binding site identification process through these co-solvent mapping methods.

Automated Computational Detection, Quantitation, and Mapping of Mitosis in Whole-Slide Images for Clinically Actionable Surgical Pathology Decision Support

Background: Determining mitotic index by counting mitotic figures (MFs) microscopically from tumor areas with most abundant MF (hotspots [HS]) produces a prognostically useful tumor grading biomarker. However, interobserver concordance identifying MF and HS can be poorly reproducible. Immunolabeling MF, coupled with computer-automated counting by image analysis, can improve reproducibility. A computational system for obtaining MF values across digitized whole-slide images (WSIs) was sought that would minimize impact of artifacts, generate values clinically relatable to counting ten high-power microscopic fields of view typical in conventional microscopy, and that would reproducibly map HS topography. Materials and Methods: Relatively low-resolution WSI scans (0.50 µm/pixel) were imported in grid-tile format for feature-based MF segmentation, from naturally occurring canine melanomas providing a wide range of proliferative activity. MF feature extraction conformed to anti-phospho-histone H3-immunolabeled mitotic (M) phase cells. Computer vision image processing was established to subtract key artifacts, obtain MF counts, and employ rotationally invariant feature extraction to map MF topography. Results: The automated topometric HS (TMHS) algorithm identified mitotic HS and mapped select tissue tiles with greatest MF counts back onto WSI thumbnail images to plot HS topographically. Influence of dye, pigment, and extraneous structure artifacts was minimized. TMHS diagnostic decision support included image overlay graphics of HS topography, as well as a spreadsheet and plot of tile-based MF count values. TMHS performance was validated examining both mitotic HS counting and mapping functions. Significantly correlated TMHS MF mapping and metrics were demonstrated using repeat analysis with WSI in different orientation (R2 = 0.9916) and by agreement with a pathologist (R2 = 0.8605) as well as through assessment of counting function using an independently tuned object counting algorithm (OCA) (R2 = 0.9482). Limits of agreement analysis support method interchangeability. MF counts obtained led to accurate patient survival prediction in all (n = 30) except one case. By contrast, more variable performance was documented when several pathologists examined similar cases using microscopy (pair-wise correlations, rho range = 0.7597-0.9286). Conclusions: Automated TMHS MF segmentation and feature engineering performance were interchangeable with both observer and OCA in digital mode. Moreover, enhanced HS location accuracy and superior method reproducibility were achieved using the automated TMHS algorithm compared to the current practice employing clinical microscopy.

Computational mapping of redox-switchable metal complexes based on ferrocene derivatives.

DFT calculations were used to capture the properties of redox-switchable metal complexes relevant to the ring-opening polymerisation of cyclic esters by varying the metals, donors, linkers, and substituents in both accessible ferrocene oxidation states. A map of this chemical space highlights that modifying the ligand architecture and the metal has a larger impact on structural changes than changing the oxidation state of the ferrocene backbone.

Automating Areas of Interest Analysis in Mobile Eye Tracking Experiments based on Machine Learning.

For an in-depth, AOI-based analysis of mobile eye tracking data, a preceding gaze assign-ment step is inevitable. Current solutions such as manual gaze mapping or marker-based approaches are tedious and not suitable for applications manipulating tangible objects. This makes mobile eye tracking studies with several hours of recording difficult to analyse quan-titatively. We introduce a new machine learning-based algorithm, the computational Gaze-Object Mapping (cGOM), that automatically maps gaze data onto respective AOIs. cGOM extends state-of-the-art object detection and segmentation by mask R-CNN with a gaze mapping feature. The new algorithm’s performance is validated against a manual fixation-by-fixation mapping, which is considered as ground truth, in terms of true positive rate (TPR), true negative rate (TNR) and efficiency. Using only 72 training images with 264 labelled object representations, cGOM is able to reach a TPR of approx. 80% and a TNR of 85% compared to the manual mapping. The break-even point is reached at 2 hours of eye tracking recording for the total procedure, respectively 1 hour considering human working time only. Together with a real-time capability of the mapping process after completed train-ing, even hours of eye tracking recording can be evaluated efficiently. (Code and video examples have been made available at: https://gitlab.ethz.ch/pdz/cgom.git)

Emergent neural turing machine and its visual navigation

Traditional Turing Machines (TMs) are symbolic whose hand-crafted representations are static and limited. Developmental Network 1 (DN-1) uses emergent representation to perform Turing Computation. But DN-1 lacks hierarchy in its internal representations, and is hard to handle the complex visual navigation tasks. In this paper, we improve DN-1 with several new mechanisms and presenta new emergent neural Turing Machine — Developmental Network 2 (DN-2). By neural, we mean that the control of the TM has neurons as basic computing elements. The major novelty of DN-2 over DN-1 is that the representational hierarchy inside DN-2 is emergent and fluid. DN-2 grows complex hierarchies by dynamically allowing initialization of neurons with different ranges of connection. We present a complex task — vision guided navigation in simulated and natural worlds using DN-2. A major function that has not been demonstrated before is that the hierarchy enables attention that disregards distracting features based on the navigation context. In simulated navigation experiments, DN-2 can perform with no errors, and in real-world navigation experiments, the error rate is only 0.78%. These experimental results showed that DN-2 successfully learned rules of navigation with image inputs.

A game-semantic model of computation

The present paper introduces a novel notion of ‘(effective) computability,’ called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church–Turing computability), non-inductive, non-axiomatic manner and shows, as a main technical achievement, that viable strategies are Turing complete. Consequently, we have given a mathematical foundation of computation in the same sense as Turing machines but beyond computation on natural numbers, e.g., higher-order computation, in a more abstract fashion. As immediate corollaries, some of the well-known theorems in computability theory such as the smn theorem and the first recursion theorem are generalized. Notably, our game-semantic framework distinguishes high-level computational processes that operate directly on mathematical objects such as natural numbers (not on their symbolic representations) and their symbolic implementations that define their ‘computability,’ which sheds new light on the very concept of computation. This work is intended to be a stepping stone toward a new mathematical foundation of computation, intuitionistic logic and constructive mathematics.

Measuring Sustainable Development Goals at a Local Level: A Case of a Metropolitan Area in Romania

Metropolitan areas became the breeding ground for economic, political, and cultural concentration as well as for creativity and innovation. Therefore, sustainability within the urban dimension plays a crucial role in the overall success to attain the SDGs (Sustainable Development Goals) and their targets under the 2030 Agenda for Sustainable Development in 2015. Nevertheless, for cities, regions, or countries to monitor and measure their progress, there is a need for harmonized and reliable indicators. Consequently, the current study addresses sustainability on a local level by measuring the extent to which a Romanian metropolitan area achieves the SDGs agreed to in 2015 by the 193-member states of the United Nations. The paper analyses 16 out of the 17 SD (Sustainable Development) goals as the goal titled “Life below water” was not applicable. Relying on mainly quantitative data, we used the method of normalization and aggregation based on the arithmetic mean, which helped us to calculate the scores attained by each of the component localities of the metropolitan area within the SDGs and their overall SDG index. Next to this, the study combines the quantitative data analysis with a GIS (Geographic Information System) computer mapping technique. The results show that the municipality achieved the best results in the metropolitan area and a vertical development process from west to the east prevails. Measuring progress through a well-defined set of indicators and an optimization technique proved to be crucial in defining attainments’ levels within the metropolitan area.

Ultrafast Single-Cell Level Enzymatic Tumor Profiling.

In the context of tumor analysis, the implementation of precision medicine requires on-time clinical measurements, which requires rapid large-scale single-cell screening that obtains cell population distributions and functions in tumors to determine disease progression for therapeutics. In this study, a high-throughput screening (HTS) platform integrating optical fluorescence detectors and a computational method was developed as a droplet-based microfluidic flow cytometer (Droplet-μFC) to comprehensively analyze multiple proteolytic activities of a patient-derived tumor (with ∼0.5-2 M cells) at single-cell resolution within 2 h. The data-driven analytical method identified distinct cell types and status through protease profiling with high precision. Multiple protease activities of single cells harvested from a tumor were thus determined with a throughput of ∼100 cells per second. This platform was used to screen protease activities of a wide range of cell types, forming a library. With the development of advanced computational clustering and cell mapping, rapid quantitative tumor profiling with a comprehensive description of cell population distributions and functions could be obtained for clinical treatments.

MR Venous Flow in Sigmoid Sinus Diverticulum.

Case reports demonstrate that coiling of a sigmoid sinus diverticulum can treat pulsatile tinnitus. We hypothesized that MR imaging 4D flow and computational fluid dynamics would reveal distinct blood flow patterns in the venous outflow tract in these patients. Patients with pulsatile tinnitus of suspected venous etiology underwent MR imaging at 3T, using venous phase contrast-enhanced MR angiography, 4D flow, and 2D phase contrast. The contrast-enhanced MRA contours were evaluated to determine the presence and extent of a sigmoid sinus diverticulum. Computational fluid dynamics analysis was performed using the 4D flow inlet flow and the luminal contours from contrast-enhanced MRA as boundary conditions. In addition, computational fluid dynamics was performed for the expected post treatment conditions by smoothing the venous geometry to exclude the sigmoid sinus diverticulum from the anatomic boundary conditions. Streamlines were generated from the 4D flow and computational fluid dynamics velocity maps, and flow patterns were examined for the presence of rotational components. Twenty-five patients with pulsatile tinnitus of suspected venous etiology and 10 control subjects were enrolled. Five (20%) of the symptomatic subjects had sigmoid sinus diverticula, all associated with an upstream stenosis. In each of these patients, but none of the controls, a stenosis-related flow jet was directed toward the opening of the sigmoid sinus diverticulum with rotational flow patterns in the sigmoid sinus diverticulum and parent sigmoid sinus on both 4D flow and computational fluid dynamics. Consistent patterns of blood flow can be visualized in a sigmoid sinus diverticulum and the parent sinus using 4D flow and computational fluid dynamics. Strong components of rotational blood flow were seen in subjects with sigmoid sinus diverticula that were absent in controls.

Noise-Based Logic Gates by Operations on the Reference System

We propose a new, low-complexity solution to realize multi-input-bit gates acting on exponentially large superpositions in noise-based logic processors. Two examples are shown, the NOT gate and the CNOT gate. The operations can be executed and repeated with polynomial time and hardware complexity. The lack of a solution for this problem had been one of the major issues prohibiting the efficient realization of Shor’s algorithm by Instantaneous Noise-Based Logic, which runs on a classical Turing computer with a true random number generator. With the method described in this paper, we are one step closer to this goal.

Investigations on the approximability and computability of the Hilbert transform with applications

It was recently shown that on a large class of important Banach spaces there exist no linear methods which are able to approximate the Hilbert transform from samples of the given function. This implies that there is no linear algorithm for calculating the Hilbert transform which can be implemented on a digital computer and which converges for all functions from the corresponding Banach spaces. The present paper develops a much more general framework which also includes non-linear approximation methods. All algorithms within this framework have only to satisfy an axiom which guarantees the computability of the algorithm based on given samples of the function. The paper investigates whether there exists an algorithm within this general framework which converges to the Hilbert transform for all functions in these Banach spaces. It is shown that non-linear methods give actually no improvement over linear methods. Moreover, the paper discusses some consequences regarding the Turing computability of the Hilbert transform and the existence of computational bases in Banach spaces.