Randomness and Computability

<p>This thesis establishes significant new results in the area of algorithmic randomness. These results elucidate the deep relationship between randomness and computability. A number of results focus on randomness for finite strings. Levin introduced two functions which measure the randomness of finite strings. One function is derived from a universal monotone machine and the other function is derived from an optimal computably enumerable semimeasure. Gacs proved that infinitely often, the gap between these two functions exceeds the inverse Ackermann function (applied to string length). This thesis improves this result to show that infinitely often the difference between these two functions exceeds the double logarithm. Another separation result is proved for two different kinds of process machine. Information about the randomness of finite strings can be used as a computational resource. This information is contained in the overgraph. Muchnik and Positselsky asked whether there exists an optimal monotone machine whose overgraph is not truth-table complete. This question is answered in the negative. Related results are also established. This thesis makes advances in the theory of randomness for infinite binary sequences. A variant of process machines is used to characterise computable randomness, Schnorr randomness and weak randomness. This result is extended to give characterisations of these types of randomness using truthtable reducibility. The computable Lipschitz reducibility measures both the relative randomness and the relative computational power of real numbers. It is proved that the computable Lipschitz degrees of computably enumerable sets are not dense. Infinite binary sequences can be regarded as elements of Cantor space. Most research in randomness for Cantor space has been conducted using the uniform measure. However, the study of non-computable measures has led to interesting results. This thesis shows that the two approaches that have been used to define randomness on Cantor space for non-computable measures: that of Reimann and Slaman, along with the uniform test approach first introduced by Levin and also used by Gacs, Hoyrup and Rojas, are equivalent. Levin established the existence of probability measures for which all infinite sequences are random. These measures are termed neutral measures. It is shown that every PA degree computes a neutral measure. Work of Miller is used to show that the set of atoms of a neutral measure is a countable Scott set and in fact any countable Scott set is the set of atoms of some neutral measure. Neutral measures are used to prove new results in computability theory. For example, it is shown that the low computable enumerable sets are precisely the computably enumerable sets bounded by PA degrees strictly below the halting problem. This thesis applies ideas developed in the study of randomness to computability theory by examining indifferent sets for comeager classes in Cantor space. A number of results are proved. For example, it is shown that there exist 1-generic sets that can compute their own indifferent sets.</p>

Randomness and Computability

<p>This thesis establishes significant new results in the area of algorithmic randomness. These results elucidate the deep relationship between randomness and computability. A number of results focus on randomness for finite strings. Levin introduced two functions which measure the randomness of finite strings. One function is derived from a universal monotone machine and the other function is derived from an optimal computably enumerable semimeasure. Gacs proved that infinitely often, the gap between these two functions exceeds the inverse Ackermann function (applied to string length). This thesis improves this result to show that infinitely often the difference between these two functions exceeds the double logarithm. Another separation result is proved for two different kinds of process machine. Information about the randomness of finite strings can be used as a computational resource. This information is contained in the overgraph. Muchnik and Positselsky asked whether there exists an optimal monotone machine whose overgraph is not truth-table complete. This question is answered in the negative. Related results are also established. This thesis makes advances in the theory of randomness for infinite binary sequences. A variant of process machines is used to characterise computable randomness, Schnorr randomness and weak randomness. This result is extended to give characterisations of these types of randomness using truthtable reducibility. The computable Lipschitz reducibility measures both the relative randomness and the relative computational power of real numbers. It is proved that the computable Lipschitz degrees of computably enumerable sets are not dense. Infinite binary sequences can be regarded as elements of Cantor space. Most research in randomness for Cantor space has been conducted using the uniform measure. However, the study of non-computable measures has led to interesting results. This thesis shows that the two approaches that have been used to define randomness on Cantor space for non-computable measures: that of Reimann and Slaman, along with the uniform test approach first introduced by Levin and also used by Gacs, Hoyrup and Rojas, are equivalent. Levin established the existence of probability measures for which all infinite sequences are random. These measures are termed neutral measures. It is shown that every PA degree computes a neutral measure. Work of Miller is used to show that the set of atoms of a neutral measure is a countable Scott set and in fact any countable Scott set is the set of atoms of some neutral measure. Neutral measures are used to prove new results in computability theory. For example, it is shown that the low computable enumerable sets are precisely the computably enumerable sets bounded by PA degrees strictly below the halting problem. This thesis applies ideas developed in the study of randomness to computability theory by examining indifferent sets for comeager classes in Cantor space. A number of results are proved. For example, it is shown that there exist 1-generic sets that can compute their own indifferent sets.</p>

The Role of 2D Fast Fourier Transform and High Pass Filter in Regional and Residual Anomaly Separation in Gravity

Regional and residual Separation anomaly is one thing that must do in gravity processing data. It is important before calculating the depth of anomaly by power spectrum. There are several ways to do this, one of them is using 2D Fast Fourier Transform (FFT). 2D FFT will calculate the two-dimensional power of the gravity map (Bouger anomaly) to change the spatial domain into the wavenumber domain. 2D FFT result has no unit because it works in the wavenumber domain. Power spectrum do in wavenumber domain map. Besides that, to make the wavenumber map in the frequency domain, it should be convolved with some filter (high–pass filter) and then inverse to separate the regional and the residual map. The design of the filter matrix depends on the number of the data and the location of anomalies will be enhanced. It will influence the separation result. The best result gets from the trial and error process. 2D FFT is act like Upward Continuation or Polynomial Fitting in the gravity method with the simple process. In this paper, the process fully done in Python. Python is an effective and simple language programming because it has many modules to support the processing and covering the big data. It also gives the flexibility to the researcher to determine the specific location that will be enhanced

Analisis Kualitatif Kandungan Fenolik dalam Fraksi Etil Asetat dan Fraksi Metanol dari Ekstrak Kulit Jagung (Zea mays L.)

ABSTRAKProduksi tanaman jagung yang semakin meningkat menyebabkan peningkatan limbah kulit jagung semakin tinggi. Kulit jagung dapat dimanfaatkan dalam bidang kesehatan dan berpotensi sebagai antioksidan. Kulit jagung mengandung senyawa fenolik dan flavonoid yang dapat bertindak sebagai antioksidan. Tujuan dari penelitian ini adalah untuk mengetahui kandungan senyawa pada fenolikfraksi etil asetat dan fraksi metanol kulit jagung. Ekstraksi kulit jagung dilakukan dengan metode maserasi menggunakan pelarut etanol 96%. Fraksinasi ekstrak etanol kulit jagung dilakukan dengan fraksinasi bertingkat menggunakan pelarut metanol dan etil asetat. Kedua fraksi yang diperoleh kemudian dianalisis secara kualitatif dengan metode Kromatografi Lapis Tipis. Fase diam yang digunakan adalah plat silica gel G60F254 dan fase gerak yang digunakan adalah kombinasi eluen kloroform: etil asetat: n-butanol: asam format (5:2:2:1). Hasil pemisahan ditandai dengan munculnya noda bercak saat diamati dengan sinar UV 254 nm dan 366 nm. Nilai Rf bercak yang muncul kemudian dihitung lalu dibandingkan dengan nilai Rf literatur untuk mengidentifikasikan senyawa yang terpisah. Hasil analisis kualitatif fraksi etil asetat dan fraksi metanol kulit jagung menunjukkan keberadaan senyawa fenolik. Hasil ini ditunjukkan dengan munculnya noda bercak dengan nilai Rf 0,75 yang memiliki kemiripan dengan nilai Rf asam galat (0,76). Kata kunci : Kulit jagung; Kromatografi lapis tipis; Analisis kualitatif. ABSTRACTCorn production keeps increasing causing increasing in corn husk waste. Cornhusk can be used in medical field and have potential as an antioxidant. Cornhusk contains phenol and flavonoid metabolites that can act as antioxidants. The aim of this study is to determine the presence of phenol metabolites in ethyl acetate and methanol fraction of cornhusk. Cornhusk extraction was carried out by a maceration method using ethanol 96%. Fractionation of ethanolic cornhusk extract was carried out by liquid-liquid extraction using a separating funnel with methanol and ethyl acetate solvent. The two fractions then analyzed qualitative by Thin Layer Chromatography. The stationary phase used is silica gel G60F254. The mobile phase used is a combination of chloroform: ethyl acetate: n-butanol: formic acid (5:2:2:1). The separation result marked by the presence of stains when observed by UV 254 nm and 366 nm light. The Rf value then measured and compared to Rf value in the literature to determine the separated substance. The qualitative analysis result of corn husk ethyl acetate fraction and methanol fraction indicated the presence of phenolic metabolites. This result is showed by the presence of stain with Rf value 0,75 that has similarity with Rf value of gallic acid (0,76). Keywords : Cornhusk; Thin layer chromatography; Qualitative analysis.

On the regularity of Cauchy hypersurfaces and temporal functions in closed cone structures

We complement our work on the causality of upper semi-continuous distributions of cones with some results on Cauchy hypersurfaces. We prove that every locally stably acausal Cauchy hypersurface is stable. Then we prove that the signed distance [Formula: see text] from a spacelike hypersurface [Formula: see text] is, in a neighborhood of it, as regular as the hypersurface, and by using this fact we give a proof that every Cauchy hypersurface is the level set of a Cauchy temporal (and steep) function of the same regularity as the hypersurface. We also show that in a globally hyperbolic closed cone structure, compact spacelike hypersurfaces with boundary can be extended to Cauchy spacelike hypersurfaces of the same regularity. We end the work with a separation result and a density result.

Unstructured Grid based Fuzzy Cooperative Resistivity Tomography for Electrical and Electromagnetic data

&lt;p&gt;There are many inversion algorithms that have been developed in the literature to obtain the resistivity distribution of the subsurface. Recovered resistivity values are usually lower/higher than the actual resistivity as a consequence of the inversion algorithms. As a consequence, Identification of geologic units based on resistivity distribution can be done on a relative scale. In general, identification of different geologic units is a post step inversion process based on resistivity distribution in the study region.&amp;#160; I have presented a technique to enhance the resistivity image using cooperative inversion (named as fuzzy cooperative resistivity tomography) where two additional input parameters are added as the number of geologic units in the model (i.e. number of cluster) and the cluster center values of the geologic units (mean resistivity value of each geologic unit). Fuzzy cooperative resistivity tomography fulfills three needs: (1) to obtain a resistivity model which will satisfy the fitting between measured and modeled data, (2) the recovered resistivity model will be guided by additional a priori parametric information, and (3) resistivity distribution and geologic separation will be accomplished simultaneously (i.e. no post inversion step will be needed). Fuzzy cooperative resistivity tomography is based on fuzzy c-means clustering technique which is an unsupervised machine learning algorithm. The highest membership value which is a direct outcome from the FCRT corresponds to a geology separation result. To obtain a geology separation result, I adopted the defuzzification method to assign a single geologic unit for each model cell based on the membership values. Various synthetic and field example data show that FCRT is an effective approach to differentiate between various geologic units. However, I have also noted that this approach is only effective when measured data sets are sensitive to particular geologic units. This is the limitation of the presented FCRT.&lt;/p&gt;

Pathways of microplastics in soils - Detection of microplastic contents in compost using a thermal decomposition method

&lt;p&gt;&lt;span&gt;The ubiquitous presence of unintended plastics in the environment has been an issue in scientific studies and public debate in the last years. It is well known that oxidative degradation and subsequent fragmentation, caused by UV-radiation, aging and abrasion lead to the decomposition of larger plastic products into microplastics (MP). Possible effects of these MP on ecosystems are still unclear. Recent studies on MP findings are focused mainly on aquatic systems, while little is known about MP in terrestrial ecosystems. Fermentation residues, sewage sludge and compost represent an input path of plastics in soils through targeted application in agriculture. For this reason, analysis of the total content of plastic in organic fertilizers as a sink and source of MP in ecosystems is of high interest.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;In 2017, approximately 14.2 million tons of biodegradable waste were collected, from which 3.9 million tons of compost was produced. Improper waste separation result in plastic fragments in the biowaste, some of which end up in the compost and might be degrade to MP. In Germany, compost is used as fertilizer in agriculture and landscape design, hence MP could enter the soil by this pathway. Spectroscopic methods such as Raman or FTIR are not suitable for determining the mass content of microplastic, as these output a particle number.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;Therefore, we show the application of ThermoExtractionDesorption-GasChromatography-MassSpectrometry (TED-GC-MS) as a fast, integral analytical technique, which in contrast to the spectroscopic methods does not measure the number of particles but a mass content. The sample is pyrolyzed to 600&amp;#176;C in a nitrogen atmosphere and an excerpt of the pyrolysis gases is collected on a solid phase adsorber. Afterwards, the decomposition gases are desorbed and measured in a GC-MS system. Characteristic pyrolysis products of each polymer can be used to identify the polymer type and determine the mass contents in the present sample. This method is well established for the analysis of MP in water filtrate samples. Here, we will first demonstrate the use of TED-GC-MS for compost.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;This current study will also give inside in various important aspects of sample preparation, which include a meaningful size fractionation, a necessary density separation regarding the removal of inorganic contents and at finally a homogenization.&lt;/span&gt;&lt;/p&gt;

Separation of Monazite from Placer Deposit by Magnetic Separation

In this study, mineralogical analysis and beneficiation experiments were conducted using a placer deposit of North Korea, on which limited information was available, to confirm the feasibility of development. Rare earth elements (REEs) have vital applications in modern technology and are growing in importance in the fourth industrial revolution. However, the price of REEs is unstable due to the imbalance between supply and demand, and tremendous efforts are being made to produce REEs sustainably. One of them is the evaluation of new rare earth mines and the verification of their feasibility. As a result of a mineralogical analysis, in this placer deposit, monazite and some amount of xenotime were the main REE-bearing minerals. Besides these minerals, ilmenite and zircon were the target minerals to be concentrated. Using a magnetic separation method at various magnetic intensities, paramagnetic minerals, ilmenite (0.8 T magnetic product), and monazite/xenotime (1.0–1.4 T magnetic product) were recovered selectively. Using a magnetic separation result, the beneficiation process was conducted with additional gravity separation for zircon to produce a valuable mineral concentrate. The process resulted in three kinds of mineral concentrates (ilmenite, REE-bearing mineral, and zircon). The content of ilmenite increased from 32.5% to 90.9%, and the total rare earth oxide (TREO) (%) of the REE-bearing mineral concentrates reached 45.0%. The zircon concentrate, a by-product of this process, had a Zr grade of 42.8%. Consequently, it was possible to produce concentrates by combining relatively simple separation processes compared to the conventional process for rare earth placer deposit and confirmed the possibility of mine development.

A SEPARATION RESULT FOR COUNTABLE UNIONS OF BOREL RECTANGLES

We provide dichotomy results characterizing when two disjoint analytic binary relations can be separated by a countable union of ${\bf{\Sigma }}_1^0 \times {\bf{\Sigma }}_\xi ^0$ sets, or by a ${\bf{\Pi }}_1^0 \times {\bf{\Pi }}_\xi ^0$ set.

Improvement of the recycling of plastics in lightweight packaging treatment plants by a process control concept

In Germany, only approximately 30% by mass of plastics from lightweight packaging waste is recycled; 65% by mass is transferred to inferior residual fractions (sorting residue and mixed plastics), which are currently only utilized thermally. An increase in the recycling of valuable resources in the sense of material recycling would both contribute to the saving of resources and improve the economic situation of plant operators. It is generally known from operating and planning experience that fluctuation in the amount of material loaded into the sorting process is one of the main reasons for suboptimal recycling quotas. In particular, overfilling in the input stream leads to a deterioration of the separation result of the entire process. A novel process control concept envisages equalizing the material flow in such a way that all separation steps are operated in the intended design range. For the example of a lightweight packaging treatment process, the requirements and technological solutions for a sensor-based process control concept will be presented.