Neuronal Correlation Parameter in the Idea of Thermodynamic Entropy of an N-Body Gravitationally Bounded System

Understanding how the brain encodes information and performs computation requires statistical and functional analysis. Given the complexity of the human brain, simple methods that facilitate the interpretation of statistical correlations among different brain regions can be very useful. In this report we introduce a numerical correlation measure that may serve the interpretation of correlational neuronal data, and may assist in the evaluation of different brain states. The description of the dynamical brain system, through a global numerical measure may indicate the presence of an action principle which may facilitate a application of physics principles in the study of the human brain and cognition

Products in Categories without Uniqueness of cod and dom

The paper introduces Cartesian products in categories without uniqueness of cod and dom. It is proven that set-theoretical product is the product in the category Ens [7].This work has been supported by the Polish Ministry of Science and Higher Education project “Managing a Large Repository of Computer-verified Mathematical Knowledge” (N N519 385136).Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok PolandGrzegorz Bancerek. König’s theorem. Formalized Mathematics, 1(3):589-593, 1990.Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Beata Madras. Basic properties of objects and morphisms. Formalized Mathematics, 6(3):329-334, 1997.Zbigniew Semadeni and Antoni Wiweger. Wstęp do teorii kategorii i funktorów, volume 45 of Biblioteka Matematyczna. PWN, Warszawa, 1978.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Andrzej Trybulec. Many sorted sets. Formalized Mathematics, 4(1):15-22, 1993.Andrzej Trybulec. Categories without uniqueness of cod and dom. Formalized Mathematics, 5(2):259-267, 1996.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990

Unification and Logarithmic Space

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof theory and more specifically linear logic and Geometry of Interaction. We show how unification can be used to build a model of computation by means of specific subalgebras associated to finite permutations groups. We then prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. We also show that the construction can naturally represent pointer machines, an intuitive way of understanding logarithmic space computing

Spatial Random Sampling: A Structure-Preserving Data Sketching Tool

Random column sampling is not guaranteed to yield data sketches that preserve the underlying structures of the data and may not sample sufficiently from less-populated data clusters. Also, adaptive sampling can often provide accurate low rank approximations, yet may fall short of producing descriptive data sketches, especially when the cluster centers are linearly dependent. Motivated by that, this paper introduces a novel randomized column sampling tool dubbed Spatial Random Sampling (SRS), in which data points are sampled based on their proximity to randomly sampled points on the unit sphere. The most compelling feature of SRS is that the corresponding probability of sampling from a given data cluster is proportional to the surface area the cluster occupies on the unit sphere, independently from the size of the cluster population. Although it is fully randomized, SRS is shown to provide descriptive and balanced data representations. The proposed idea addresses a pressing need in data science and holds potential to inspire many novel approaches for analysis of big data

Qualitative Case Studies in Operations Management: Trends, Research Outcomes, And Future Research Implications

Our study examines the state of qualitative case studies in operations management. Five main operations management journals are included for their impact on the field. They are in alphabetical order: Decision Sciences, International Journal of Operations and Production Management, Journal of Operations Management, Management Science, and Production and Operations Management. The qualitative case studies chosen were published between 1992 and 2007. With an increasing trend toward using more qualitative case studies, there have been meaningful and significant contributions to the field of operations management, especially in the area of theory building. However, in many of the qualitative case studies we reviewed, sufficient details in research design, data collection, and data analysis were missing. For instance, there are studies that do not offer sampling logic or a description of the analysis through which research out-comes are drawn. Further, research protocols for doing inductive case studies are much better developed compared to the research protocols for doing deductive case studies. Consequently, there is a lack of consistency in the way the case method has been applied. As qualitative researchers, we offer suggestions on how we can improve on what we have done and elevate the level of rigor and consistency

Wetting gradient induced separation of emulsions: A combined experimental and lattice Boltzmann computer simulation study

Guided motion of emulsions is studied via combined experimental and theoretical investigations. The focus of the work is on basic issues related to driving forces generated via a step-wise (abrupt) change in wetting properties of the substrate along a given spatial direction. Experiments on binary emulsions unambiguously show that selective wettability of the one of the fluid components (water in our experiments) with respect to the two different parts of the substrate is sufficient in order to drive the separation process. These studies are accompanied by approximate analytic arguments as well as lattice Boltzmann computer simulations, focusing on effects of a wetting gradient on internal droplet dynamics as well as its relative strength compared to volumetric forces driving the fluid flow. These theoretical investigations show qualitatively different dependence of wetting gradient induced forces on contact angle and liquid volume in the case of an open substrate as opposed to a planar channel. In particular, for the parameter range of our experiments, slit geometry is found to give rise to considerably higher separation forces as compared to open substrate.Comment: 34 pages, 12 figure

The strong influence of substrate conductivity on droplet evaporation

We report the results of physical experiments that demonstrate the strong influence of the thermal conductivity of the substrate on the evaporation of a pinned droplet. We show that this behaviour can be captured by a mathematical model including the variation of the saturation concentration with temperature, and hence coupling the problems for the vapour concentration in the atmosphere and the temperature in the liquid and the substrate. Furthermore, we show that including two ad hoc improvements to the model, namely a Newton's law of cooling on the unwetted surface of the substrate and the buoyancy of water vapour in the atmosphere, give excellent quantitative agreement for all of the combinations of liquid and substrate considered

Algorithmic Randomness as Foundation of Inductive Reasoning and Artificial Intelligence

This article is a brief personal account of the past, present, and future of algorithmic randomness, emphasizing its role in inductive inference and artificial intelligence. It is written for a general audience interested in science and philosophy. Intuitively, randomness is a lack of order or predictability. If randomness is the opposite of determinism, then algorithmic randomness is the opposite of computability. Besides many other things, these concepts have been used to quantify Ockham's razor, solve the induction problem, and define intelligence.Comment: 9 LaTeX page