On the computational complexity of the languages of general symbolic dynamical systems and beta-shifts

AbstractWe consider the computational complexity of languages of symbolic dynamical systems. In particular, we study complexity hierarchies and membership of the non-uniform class P/poly. We prove: 1.For every time-constructible, non-decreasing function t(n)=ω(n), there is a symbolic dynamical system with language decidable in deterministic time O(n2t(n)), but not in deterministic time o(t(n)).2.For every space-constructible, non-decreasing function s(n)=ω(n), there is a symbolic dynamical system with language decidable in deterministic space O(s(n)), but not in deterministic space o(s(n)).3.There are symbolic dynamical systems having hard and complete languages under ≤mlogs- and ≤mp-reduction for every complexity class above LOGSPACE in the backbone hierarchy (hence, P-complete, NP-complete, coNP-complete, PSPACE-complete, and EXPTIME-complete sets).4.There are decidable languages of symbolic dynamical systems in P/poly for every alphabet of size |Σ|≥1.5.There are decidable languages of symbolic dynamical systems not in P/poly iff the alphabet size is >1.For the particular class of symbolic dynamical systems known as β-shifts, we prove that: 1.For all real numbers β>1, the language of the β-shift is in P/poly.2.If there exists a real number β>1 such that the language of the β-shift is NP-hard under ≤Tp-reduction, then the polynomial hierarchy collapses to the second level. As NP-hardness under ≤mp-reduction implies hardness under ≤Tp-reduction, this result implies that it is unlikely that a proof of existence of an NP-hard language of a β-shift will be forthcoming.3.For every time-constructible, non-decreasing function t(n)≥n, there is a real number 1<β<2 such that the language of the β-shift is decidable in time O(n2t(logn+1)), but not in any proper time bound g(n) satisfying g(4n)=o(t(n)/16n).4.For every space-constructible, non-decreasing function s(n)=ω(n2), there is a real number 1<β<2 such that the language of the β-shift is decidable in space O(s(n)), but not in space g(n) where g is any function satisfying g(n2)=o(s(n)).5.There exists a real number 1<β<2 such that the language of the β-shift is recursive, but not context-sensitive

Genomic adaptations to cereal-based diets contribute to mitigate metabolic risk in some human populations of East Asian ancestry

Adoption of diets based on some cereals, especially on rice, signified an iconic change in nutritional habits for many Asian populations and a relevant challenge for their capability to maintain glucose homeostasis. Indeed, rice shows the highest carbohydrates content and glycemic index among the domesticated cereals and its usual ingestion represents a potential risk factor for developing insulin resistance and related metabolic diseases. Nevertheless, type 2 diabetes and obesity epidemiological patterns differ among Asian populations that rely on rice as a staple food, with higher diabetes prevalence and increased levels of central adiposity observed in people of South Asian ancestry rather than in East Asians. This may be at least partly due to the fact that populations from East Asian regions where wild rice or other cereals such as millet have been already consumed before their cultivation and/or were early domesticated have relied on these nutritional resources for a period long enough to have possibly evolved biological adaptations that counteract their detrimental side effects. To test such a hypothesis, we compared adaptive evolution of these populations with that of control groups from regions where the adoption of cereal-based diets occurred many thousand years later and which were identified from a genome-wide dataset including 2,379 individuals from 124 East Asian and South Asian populations. This revealed selective sweeps and polygenic adaptive mechanisms affecting functional pathways involved in fatty acids metabolism, cholesterol/triglycerides biosynthesis from carbohydrates, regulation of glucose homeostasis, and production of retinoic acid in Chinese Han and Tujia ethnic groups, as well as in people of Korean and Japanese ancestry. Accordingly, long-standing rice- and/or millet-based diets have possibly contributed to trigger the evolution of such biological adaptations, which might represent one of the factors that play a role in mitigating the metabolic risk of these East Asian populations

Dynamical Directions in Numeration

International audienceWe survey definitions and properties of numeration from a dynamical point of view. That is we focuse on numeration systems, their associated compactifications, and the dynamical systems that can be naturally defined on them. The exposition is unified by the notion of fibred numeration system. A lot of examples are discussed. Various numerations on natural, integral, real or complex numbers are presented with a special attention payed to beta-numeration and its generalisations, abstract numeration systems and shift radix systems. A section of applications ends the paper

Combinatorics of Pisot Substitutions

Siirretty Doriast

Visual Analysis Algorithms for Embedded Systems

The main contribution of this thesis is the design and development of an optimized framework to realize the deep neural classifiers on the embedded platforms. Deep convolutional networks exhibit unmatched performance in image classification. However, these deep classifiers demand huge computational power and memory storage. That is an issue on embedded devices due to limited onboard resources. The computational demand of neural networks mainly stems from the convolutional layers. A significant improvement in performance can be obtained by reducing the computational complexity of these convolutional layers, making them realizable on embedded platforms. In this thesis, we proposed a CUDA (Compute Unified Device Architecture)-based accelerated scheme to realize the deep architectures on the embedded platforms by exploiting the already trained networks. All required functions and layers to replicate the trained neural networks were implemented and accelerated using concurrent resources of embedded GPU. Performance of our CUDA-based proposed scheme was significantly improved by performing convolutions in the transform domain. This matrix multiplication based convolution was also compared with the traditional approach to analyze the improvement in inference performance. The second part of this thesis focused on the optimization of the proposed framework. The flow of our CUDA-based framework was optimized using unified memory scheme and hardware-dependent utilization of computational resources. The proposed flow was evaluated over three different image classification networks on Jetson TX1 embedded board and Nvidia Shield K1 tablet. The performance of proposed GPU-only flow was compared with its sequential and heterogeneous versions. The results showed that the proposed scheme brought the higher performance and enabled the real-time image classification on the embedded platforms with lesser storage requirements. These results motivated us towards the realization of useful real-time classification and recognition problems on the embedded platforms. Finally, we utilized the proposed framework to realize the neural network-based automatic license plate recognition (ALPR) system on a mobile platform. This highly-precise and computationally demanding system was deployed by simplifying the flow of trained deep architecture developed for powerful desktop and server environments. A comparative analysis of computational complexity, recognition accuracy and inference performance was performed

The Significance of Evidence-based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences

In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. The second yields a strong, finitary, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically computable Tarskian truth values to the formulas of PA under the interpretation. We situate our investigation within a broad analysis of quantification vis a vis: * Hilbert's epsilon-calculus * Goedel's omega-consistency * The Law of the Excluded Middle * Hilbert's omega-Rule * An Algorithmic omega-Rule * Gentzen's Rule of Infinite Induction * Rosser's Rule C * Markov's Principle * The Church-Turing Thesis * Aristotle's particularisation * Wittgenstein's perspective of constructive mathematics * An evidence-based perspective of quantification. By showing how these are formally inter-related, we highlight the fragility of both the persisting, theistic, classical/Platonic interpretation of quantification grounded in Hilbert's epsilon-calculus; and the persisting, atheistic, constructive/Intuitionistic interpretation of quantification rooted in Brouwer's belief that the Law of the Excluded Middle is non-finitary. We then consider some consequences for mathematics, mathematics education, philosophy, and the natural sciences, of an agnostic, evidence-based, finitary interpretation of quantification that challenges classical paradigms in all these disciplines

CGiS : high-level data-parallel GPU programming

In the last few years, PC technology underwent a paradigm shift. The current trend leads aways from raising sequential performance to enhancing the available parallelism. The rapid performance increase of Graphics Processing Units (GPUs) is a part of this trend. However, it is difficult to harness the computational potential because for the longest time GPUs could be directed only through graphics APIs and in low-level code. The language CGiS has been developed to remedy this situation. CGiS is a data-parallel programming language, which offers a high-level abstraction of GPUs, letting programmers use GPUs as co-processors for massively parallel algorithms. This work presents the language and the compiler for CGiS in the context of general purpose programming on GPUs (GPGPU).Seit einigen Jahren zeichnet sich bei handelsüblichen PCs ein Trend weg von der Erhöhung der sequentiellen Leistung hin zur Parallelverarbeitung ab. Ein Bestandteil dieses Trends ist die rasche Leistungsentwicklung der Grafikkarten (GPUs), deren Rechenleistung die aktueller CPUs mittlerweile übertrifft. Es ist jedoch schwierig, diese Leistung auch abzurufen, da diese Geräte lange Zeit nur hardwarenah und über Grafik-APIs ansteuerbar waren. Um dies zu ändern, ist CGiS entwickelt worden, eine datenparallele Programmiersprache, die die GPUs abstrahiert und ihre Benutzung als Co-Prozessoren für massiv-datenparallele Algorithmen ermöglicht. Diese Arbeit stellt die Sprache und den Compiler im Kontext dieser Entwicklung vor