Characterization theorem for the conditionally computable real functions

The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains. The class of conditionally computable real functions with respect to the same class of operators is a proper extension of the class of uniformly computable real functions and it computes the elementary functions of calculus on their whole domains. The definition of both classes relies on certain transformations of infinitistic names of real numbers. In the present paper, the conditional computability of real functions is characterized in the spirit of Tent and Ziegler, avoiding the use of infinitistic names

Spatial stochastic predator-prey models

We consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the deterministic rate equations, on the properties of the stochastic models. Here, we outline the robust scenario obeyed by most of the lattice predator-prey models with an interaction "a' la Lotka-Volterra". We also show how a drastically different behavior can emerge as the result of a subtle interplay between long-range interactions and a nearest-neighbor exchange process.Comment: 5 pages, 2 figures. Proceedings paper of the workshop "Stochastic models in biological sciences" (May 29 - June 2, 2006 in Warsaw) for the Banach Center Publication

COMPETITION AND COOPERATION: SINO-RUSSIAN INTERACTIONS IN ASIA IN THE ERA OF GREAT POWER COMPETITION

In the great power competition–era, the United States finds itself challenged by two main adversaries: Russia and China. This is especially evident in Asia, where both rival powers seek to retain and expand their traditional political, economic, and military spheres of influence while attempting to put limits on U.S. involvement. This thesis explored the dynamics of competition and cooperation between Russia and China in order to ascertain which are stronger. To achieve this, the thesis examined Sino-Russian interactions in three specific cases: Central Asia, North Korea, and Mongolia. In the case of Central Asia, competition between Russia and China was the strongest of the three cases due to the region’s importance to both great powers. However, shared security concerns and the opposition to U.S. presence push Moscow and Beijing toward cooperation. Regarding North Korea, Russia largely follows China’s lead, recognizing shared concerns about the stability of the DPRK regime and the greater importance of the region to Beijing. Finally, in Mongolia, Moscow and Beijing cooperate for the sake of maintaining a stable and predictable neighbor, avoiding an unnecessary security dilemma. In all three cases, Russia and China were found to prefer cooperation to competition, both to ensure their peripheries’ stability and focus their efforts on the great power competition with the United States.Lieutenant, United States NavyApproved for public release. Distribution is unlimited

Renormalization-group Studies of Three Model Systems Far from Equilibrium

This thesis describes the development of analytical and computational techniques for systems far from equilibrium and their application to three model systems. Each of the model systems reaches a non-equilibrium steady state and exhibits one or more phase transitions. We first introduce a new position-space renormalization-group approach and illustrate its application using the one-dimensional fully asymmetric exclusion process. We have constructed a recursion relation for the relevant dynamic parameters for this model and have reproduced all of the important critical features of the model, including the exact positions of the critical point and the first and second order phase boundaries. The method yields an approximate value for the critical exponent v which is very close to the known value. The second major part of this thesis combines information theoretic techniques for calculating the entropy and a Monte Carlo renormalization-group approach. We have used this method to study and compare infinitely driven lattice gases. This approach enables us to calculate the critical exponents associated with the correlation length v and the order parameter /3. These results are compared to the values predicted from different field theoretic treatments of the models. In the final set of calculations, we build position-space renormalization-group recursion relations from the master equations of small clusters. By obtaining the probability distributions for these clusters numerically, we develop a mapping connecting the parameters specifying the dynamics on different length scales. The resulting flow topology in some ways mimics equilibrium features, with sinks for each phase and fixed points associated with each phase boundary. In addition, though, there are added complexities in the flows, suggesting multiple regions within the ordered phase for some values of parameters, and the presence of an extra source fixed point within the ordered phase. Thus, this study illustrates the successful applicability of position-space renormalization- group and information theoretic approaches to driven lattice gases in one and two dimensions. These methods provide new insights into the critical properties and ordering in these systems, and set the stage for further development of these approaches and their application to additional, more realistic models

STRUCTURAL INVESTIGATION OF A HIGH-CHROMIUM MATERIAL USED AS AN EXTERNAL, WORKING LAYER OF A BIMETALLIC MILL ROLLER

The bimetallic mill roller has been produced by the method of vertical axis centrifugal casting. The processes, accompanying the formation of the structure of the external (working) layer from high chromium material of the bimetallic roller have been investigated. A mathematical model for the geometry of the working layer was created. By using the MAGMA Soft software package, simulations of the processes of casting and crystallization have been made. A metallographic assessment of the microstructure has been made.

STRUCTURAL INVESTIGATION OF THE INTERMEDIATE LAYER IN A BIMETAL MILL ROLLER PRODUCED BY THE METHOD OF VERTICAL AXIS CENTRIFUGAL CASTING

Subject of the investigation is a bimetallic mill roller with external, working layer from high chromium material and inner, supporting layer from ductile cast iron. The processes, accompanying the formation of a transition layer in bimetallic castings, produced by centrifugal casting have been investigated. Attention has paid to the structural changes in the transition zone, caused by the diffusion processes occurring during the casting and crystallization

Manual adjustment of brain extraction parameters in a volumetric study

INTRODUCTION: Brain volumetry is a contemporary method used in scientific and clinical research in neurodegenerative diseases. The process can be fully automated but it allows some parameters to be manually adjusted in order to minimize errors. The purpose of the present study is to analyze the use of additional settings in the process of extracting brain tissue from the skull in volumetric assessments performed using FSL-SIENAX, to point out the most frequently used ones, and to provide recommendations for their application.MATERIAL AND METHODS: 3DT1 MRI scans of 51 patients with multiple sclerosis were processed. After conversion from the native format, brain tissue was extracted using the BET procedure. Multiple experiments were done using different parameters followed by a visual assessment of the results. Optimal values were chosen for each case. Descriptive statistical analysis was performed.RESULTS: Manual corrections of the default settings of BET were made in all studied cases. The most frequently applied parameter (100% of cases) was `-f`, which adjusts the aggressiveness of the algorithm, followed by `-B` (51%), which reduces bias field and neck voxels, `-R` (31,4%), multiple iterations of the algorithm, `-g` (25,5%), correction of the vertical gradient, `-S` (2%), removal of wrongfully identified optic nerves and eyeballs.CONCLUSION: The fully automatic volumetric assessment of the brain performed by FSL-SIENAX accelerates the workflow, but may lead to imperfections in the results. Manual adjustment trials may begin with the "-f" parameter, followed by "-Ð’", "-R", "-g", and combinations between them