Computable randomness is about more than probabilities

We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense that we consider lower expectations (or sets of probabilities) instead of classical 'precise' probabilities. Secondly, instead of binary sequences, we consider sequences whose elements take values in some finite sample space. Interestingly, we find that every sequence is computably random with respect to at least one lower expectation, and that lower expectations that are more informative have fewer computably random sequences. This leads to the intriguing question whether every sequence is computably random with respect to a unique most informative lower expectation. We study this question in some detail and provide a partial answer

Solid-State NMR Spectroscopy:Towards Structural Insights into Starch-Based Materials in the Food Industry

Solid-state NMR is a nondestructive and noninvasive technique used to study the chemical structure and dynamics of starch-based materials and to bridge the gap between structure–function relationships and industrial applications. The study of crystallinity, chemical modification, product blending, molecular packing, amylose–amylopectin ratio, end chain motion, and solvent–matrix interactions is essential for tailoring starch product properties to various applications. This article aims to provide a comprehensive and critical review of research characterizing starch-based materials using solid-state NMR, and to briefly introduce the most advanced and promising NMR strategies and hardware designs used to overcome the sensitivity and resolution issues involved in structure–function relationships

Synergistic Catalytic Effects of Alloys of Noble Metal Nanoparticles Supported on Two Different Supports:Crystalline Zeolite Sn-Beta and Carbon Nanotubes for Glycerol Conversion to Methyl Lactate

Two multifunctional catalytic systems comprising Sn-based/doped crystalline zeolite Beta were synthesized, and they were employed as heterogeneous catalysts in the selective conversion of glycerol to methyl lactate. The first catalytic system, named Au-Pd-Sn-deAl-7.2-Beta-DP, was created through the post-synthesis dealumination of the parent zeolite Beta (Si/Al = 10) using 7.2 M HNO3. Subsequently, it was grafted with 27 mmol of SnCl4, resulting in Sn-deAl-7.2-Beta. Following this, Au and Pd nanoparticles were supported on this catalyst using the deposition–precipitation (DP) method. The second catalytic system was a physical mixture of Au and Pd nanoparticles supported on functionalized carbon nanotubes (Au-Pd-F-CNTs) and Sn-containing zeolite Beta (Sn-deAl-7.2-Beta). Both catalytic systems were employed in glycerol partial oxidation to methyl lactate under the following conditions: 140 °C for 4.5 h under an air pressure of 30 bar. The Au-Pd-Sn-deAl-7.2-Beta-DP catalytic system demonstrated 34% conversion of glycerol with a 76% selectivity for methyl lactate. In contrast, the physical mixture of Au-Pd-F-CNTs and Sn-deAl-7.2-Beta exhibited higher activity, achieving 58% glycerol conversion and a nearly identical selectivity for methyl lactate (77%). The catalytic results and catalyst structure were further analyzed using various characterization techniques, such as X-ray diffraction (XRD), N2 physisorption, scanning electron microscopy (SEM), X-ray fluorescence (XRF), transmission electron microscopy (TEM), UV-vis spectroscopy, and pyridine Fourier transform infrared (FTIR). These analyses emphasized the significance of adjusting the quantity of active sites, particle size, and active sites proximity under the chosen reaction conditions.</p

Ore Genesis of the Abu Ghalaga Ferro-Ilmenite Ore Associated with Neoproterozoic Massive-Type Gabbros, South-Eastern Desert of Egypt: Evidence from Texture and Mineral Chemistry

Massif-type mafic intrusions (gabbro and anorthosite) are known for their considerable resources of vanadium-bearing iron–titanium oxide ores. Massive-type gabbroic and anorthosite rocks are frequently associated with magmatic rocks that have significant quantities of iron, titanium, and vanadium. The most promising intrusions that host Fe-Ti oxide ores are the gabbroic rocks in the south-eastern desert. The ilmenite ore deposits are hosted in arc gabbroic and anorthosite rocks. They are classified into three types, namely black ore, red ore, and disseminated ore. The black ilmenite ore is located at the deeper level, while the oxidized red ore is mainly located at or near the surface. Petrographically, the gabbro and ilmenite ores indicate a crystallization sequence of plagioclase, titaniferous pyroxene, and ilmenite. This reveals that the ilmenite is a magmatic deposit formed by the liquid gravity concentration of ilmenite following the crystallization of feldspar and pyroxene. Meanwhile, quartz, tremolite, zoisite, and opaque minerals are accessory minerals. The Fe-Ti ores are composed of ilmenite hosting exsolved hematite lamellae of variable sizes and shapes, gangue silicate minerals, and some sulfides. The X-ray diffraction (XRD) data reveal the presence of two mineral phases: ilmenite and hematite formed by the unmixing of the ferroilmenite homogeneous phase upon cooling. As a result, the ore is mostly made up of hemo-ilmenite. Using an electron microscope (SEM), as well as by observing the textures seen by the ore microscope, ilmenite is the dominant Fe-Ti oxide and contains voluminous hematite exsolved crystals. Under the scanning electron microscope, ilmenite contained intergrowths of hematite as a thin sandwich and lens shape. The formation of hematite lamellae indicates an oxidation process. Mineral chemistry-based investigations reveal late/post-magmatic activity at high temperatures. The examined ilmenite plots on the ferro-ilmenite line were created by continuous solid solution over 800 °C, whereas the analyzed magnetite and Ti-magnetite plot near the magnetite line and were formed by continuous solid solution exceeding 600 °C

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Computable de Finetti measures

We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we prove that a distribution on the unit interval is computable if and only if its moments are uniformly computable.Comment: 32 pages. Final journal version; expanded somewhat, with minor corrections. To appear in Annals of Pure and Applied Logic. Extended abstract appeared in Proceedings of CiE '09, LNCS 5635, pp. 218-23

Effective local connectivity properties

We investigate, and prove equivalent, effective versions of local connectivity and uniformly local arcwise connectivity for connected and computably compact subspaces of Euclidean space. We also prove that Euclidean continua that are computably compact and effectively locally connected are computably arcwise connected.Comment: Final versio

Computability and dynamical systems

In this paper we explore results that establish a link between dynamical systems and computability theory (not numerical analysis). In the last few decades, computers have increasingly been used as simulation tools for gaining insight into dynamical behavior. However, due to the presence of errors inherent in such numerical simulations, with few exceptions, computers have not been used for the nobler task of proving mathematical results. Nevertheless, there have been some recent developments in the latter direction. Here we introduce some of the ideas and techniques used so far, and suggest some lines of research for further work on this fascinating topic

Recent Advances in Σ-definability over Continuous Data Types

The purpose of this paper is to survey our recent research in computability and definability over continuous data types such as the real numbers, real-valued functions and functionals. We investigate the expressive power and algorithmic properties of the language of Sigma-formulas intended to represent computability over the real numbers. In order to adequately represent computability we extend the reals by the structure of hereditarily finite sets. In this setting it is crucial to consider the real numbers without equality since the equality test is undecidable over the reals. We prove Engeler's Lemma for Sigma-definability over the reals without the equality test which relates Sigma-definability with definability in the constructive infinitary language L_{omega_1 omega}. Thus, a relation over the real numbers is Sigma-definable if and only if it is definable by a disjunction of a recursively enumerable set of quantifier free formulas. This result reveals computational aspects of Sigma-definability and also gives topological characterisation of Sigma-definable relations over the reals without the equality test. We also illustrate how computability over the real numbers can be expressed in the language of Sigma-formulas

Computability of ordinary differential equations

In this paper we provide a brief review of several results about the computability of initial-value problems (IVPs) defined with ordinary differential equations (ODEs). We will consider a variety of settings and analyze how the computability of the IVP will be affected. Computational complexity results will also be presented, as well as computable versions of some classical theorems about the asymptotic behavior of ODEs.info:eu-repo/semantics/publishedVersio