Abstraction and Representational Capacity in Computational Structures

2019 ◽  
pp. 210-229
Author(s):  
Michael Weisberg
Keyword(s):  
Mathematical Models ◽  
Computational Models ◽  
Mathematical Structure ◽  
Narrative Form ◽  
Mathematical Structures ◽  
Computational Structure ◽  
Representational Capacity ◽  
Computational Structures

Michael Weisberg’s book Simulation and Similarity argued that although mathematical models are sometimes described in narrative form, they are best understood as interpreted mathematical structures. But how can a mathematical structure be causal, as many models described in narrative seem to be? This chapter argues that models with apparently narrative form are actually computational structures. It explores this suggestion in detail, examining what computational structure consists of, the resources it offers modelers, and why attempting to re-describe computational models as imaginary concrete systems fails even more dramatically than it does for mathematical models.

scholarly journals Analysis of HMAX Algorithm on Black Bar Image Dataset

Electronics ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 567
Author(s):  
Alessandro Carlini ◽  
Olivier Boisard ◽  
Michel Paindavoine
Keyword(s):  
Computational Models ◽  
Gabor Filter ◽  
Low Contrast ◽  
Computational Structure ◽  
Image Dataset ◽  
Information Pattern ◽  
Traditional Assessments ◽  
Flexible Model ◽  
Computational Structures

An accurate detection and classification of scenes and objects is essential for interacting with the world, both for living beings and for artificial systems. To reproduce this ability, which is so effective in the animal world, numerous computational models have been proposed, frequently based on bioinspired, computational structures. Among these, Hierarchical Max-pooling (HMAX) is probably one of the most important models. HMAX is a recognition model, mimicking the structures and functions of the primate visual cortex. HMAX has already proven its effectiveness and versatility. Nevertheless, its computational structure presents some criticalities, whose impact on the results has never been systematically assessed. Traditional assessments based on photographs force to choose a specific context; the complexity of images makes it difficult to analyze the computational structure. Here we present a new, general and unspecific assessment of HMAX, introducing the Black Bar Image Dataset, a customizable set of images created to be a universal and flexible model of any ‘real’ image. Results: surprisingly, HMAX demonstrates a notable sensitivity also with a low contrast of luminance. Images containing a wider information pattern enhance the performances. The presence of textures improves performance, but only if the parameterization of the Gabor filter allows its correct encoding. In addition, in complex conditions, HMAX demonstrates good effectiveness in classification. Moreover, the present assessment demonstrates the benefits offered by the Black Bar Image Dataset, its modularity and scalability, for the functional investigations of any computational models.

Computing, Philosophy and Reality

2010 ◽  
pp. 238-252
Author(s):  
Joseph Brenner
Keyword(s):  
Quantum Computing ◽  
Cellular Automata ◽  
Computational Modeling ◽  
Computational Models ◽  
Mathematical Structure ◽  
Quantum Superposition ◽  
Information Theoretic ◽  
Process View ◽  
New Interpretation ◽  
The Universe

The conjunction of the disciplines of computing and philosophy implies that discussion of computational models and approaches should include explicit statements of their underlying worldview, given the fact that reality includes both computational and non-computational domains. As outlined at ECAP08, both domains of reality can be characterized by the different logics applicable to them. A new “Logic in Reality” (LIR) was proposed as best describing the dynamics of real, non-computable processes. The LIR process view of the real macroscopic world is compared here with recent computational and information-theoretic models. Proposals that the universe can be described as a mathematical structure equivalent to a computer or by simple cellular automata are deflated. A new interpretation of quantum superposition as supporting a concept of paraconsistent parallelism in quantum computing and an appropriate ontological commitment for computational modeling are discussed.

scholarly journals Observation of a Most Phenomenal Computed Calligraphy in Quran

2016 ◽  
Vol 9 (3) ◽  
pp. 42
Author(s):  
Baback Khodadoost
Keyword(s):  
Present Article ◽  
Recent Article ◽  
Mathematical Structure ◽  
Font Size ◽  
Computational Structure ◽  
The Given ◽  
Word Frequencies ◽  
Mathematical Design

<span style="font-size: 10pt; font-family: 'Times New Roman','serif'; color: black; mso-bidi-font-size: 9.0pt; mso-fareast-font-family: 宋体; mso-themecolor: text1; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">Observation of a multifaceted mathematical-computational structure of Quran through analysis of its letter and word frequencies and important implications of such observations have been extensively explained and discussed in a recent article: </span><span style="font-size: 10pt; font-family: 'Times New Roman','serif'; color: black; mso-bidi-font-size: 8.0pt; mso-fareast-font-family: 宋体; mso-themecolor: text1; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">“Khodadoost B. (2015) The Computed Scripture: Exponentially Based Fourier Regulated Construct of Quran and its fundamentally important Consequences"</span><span style="font-size: 10pt; font-family: 'Times New Roman','serif'; color: black; mso-bidi-font-size: 9.0pt; mso-fareast-font-family: 宋体; mso-themecolor: text1; mso-font-kerning: 1.0pt; mso-ansi-language: EN-US; mso-fareast-language: ZH-CN; mso-bidi-language: AR-SA;" lang="EN-US">. In the present article we report observation of yet another facet of this mathematical structure of Quran which is a phenomenal "parametric name-printing”. This observation has been made through a systematic compute-plot algorithm which uses the given name and chapter frequencies of letters in Quran as its input and shows in the output, calligraphic printing in Arabic of the same name. Several names of God, Major Prophets, and even some physicists are shown to clearly manifest these calligraphic effects. Sensitivities of these observations to changes in letter frequencies in Quran are so high that increase or decrease of even one letter and only in one chapter of Quran can completely demolish the calligraphic effects. These astonishing observations not only are extremely important and interesting in their own right, but also point to an immensely complicated and intricate super-intelligent mathematical design of Quran and reinforce "Mathematically Fully constrained Writing" or MFCW identity of this scripture and its consequences, as have been explained in the above article.</span>

Reconstruction of Historical Timber Roofs at Žehušice Castle

2015 ◽  
Vol 1122 ◽  
pp. 19-22
Author(s):  
Rostislav Zídek ◽  
Aleš Utíkal ◽  
Ivana Utíkalová ◽  
Luděk Brdečko ◽  
Helena Brdečková
Keyword(s):  
Mathematical Models ◽  
Computational Models ◽  
Structural Systems ◽  
Static Behavior ◽  
Existing Structures ◽  
Fungal Attack ◽  
National Heritage ◽  
Distribution Of Stresses

The paper presents some aspects of the reconstruction of timber roofs at Žehušice Castle. The roofs were built at different times and using various types of structural systems. Many timber elements of the roofs have been heavily damaged by previous unprofessional alterations to them, or, more often, by neglected maintenance and subsequent fungal attack caused by massive leaking. Because of the requirements of the National Heritage Institute it was necessary to be sensitive to the existing structures and minimize changes to them during the reconstruction of the roofs. In order to successfully achieve this, it was necessary to understand the distribution of stresses in the structure and its static behavior as well as possible. Therefore, 3D computational models were developed. On the basis of the obtained results, it was decided whether roof elements would be replaced or only parts of them. However, the informative value of relatively complicated mathematical models appeared to be limited.

scholarly journals Unification of Gravity and Electromagnetism

2021 ◽  
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Mathematical Structure ◽  
Momentum Tensor ◽  
Dirac Field ◽  
Field Equations ◽  
Mathematical Structures ◽  
Gravitational Field Equations ◽  
Definition Of ◽  
Two Sides

Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are representing by two mathematical structures, symmetric and antisymmetric respectively. Einstein gravitational field equation is the symmetric mathematical structure. Electrodynamics Lagrangian is three parts, for electromagnetic field, Dirac field and interaction term. The definition of canonical energy momentum tensor was used for each term in Electrodynamics Lagrangian to construct the antisymmetric mathematical structure. Symmetric and antisymmetric gravitational field equations are two sides of the same Lagrangian

scholarly journals A New Kind of Aesthetics – The Mathematical Structure of the Aesthetic

2017 ◽  
Author(s):  
Akihiro Kubota ◽  
Hirokazu Hori ◽  
Makoto Naruse ◽  
Fuminori Akiba
Keyword(s):  
Human Activity ◽  
Category Theory ◽  
Mathematical Structure ◽  
Derived Category ◽  
New Method ◽  
Work Of Art ◽  
New Approach ◽  
Mathematical Structures ◽  
Dynamic Relations ◽  
The Aesthetic

This paper proposes a new approach to investigation into the aesthetics. Specifically, it argues that it is possible to explain the aesthetic and its underlying dynamic relations with axiomatic structure (the octahedral axiom derived category) based on contemporary mathematics &ndash;&nbsp;namely, category theory &ndash;&nbsp;and through this argument suggests the possibility for discussion about the mathematical structure of the aesthetic. If there was a way to describe the structure of aesthetics with the language of mathematical structures and mathematical axioms &ndash;&nbsp;a language completely devoid of arbitrariness &ndash;&nbsp;then we would make possible a synthetical argument about the essential human activity of &ldquo;the aesthetics&rdquo;, and we would also gain a new method and viewpoint on the philosophy and meaning of the act of creating a work of art and artistic activities. This paper presents one hypothesis as a first step in constructing the science of dynamic generative aesthetics based on axiomatic functionalism, which is in turn based on a new interdisciplinary investigation into the functional structure of aesthetics.

scholarly journals Modelling Animal Interactive Rhythms in Communication

2019 ◽  
Vol 15 ◽  
pp. 117693431882355
Author(s):  
Andrea Ravignani ◽  
Koen de Reus
Keyword(s):  
Mathematical Models ◽  
Computational Models ◽  
Animal Communication ◽  
Animal Experiments ◽  
Simulated Data ◽  
Empirical Literature ◽  
Ecological Niches ◽  
Temporal Properties ◽  
Before And After ◽  
Underlying Mechanisms

Time is one crucial dimension conveying information in animal communication. Evolution has shaped animals’ nervous systems to produce signals with temporal properties fitting their socio-ecological niches. Many quantitative models of mechanisms underlying rhythmic behaviour exist, spanning insects, crustaceans, birds, amphibians, and mammals. However, these computational and mathematical models are often presented in isolation. Here, we provide an overview of the main mathematical models employed in the study of animal rhythmic communication among conspecifics. After presenting basic definitions and mathematical formalisms, we discuss each individual model. These computational models are then compared using simulated data to uncover similarities and key differences in the underlying mechanisms found across species. Our review of the empirical literature is admittedly limited. We stress the need of using comparative computer simulations – both before and after animal experiments – to better understand animal timing in interaction. We hope this article will serve as a potential first step towards a common computational framework to describe temporal interactions in animals, including humans.

scholarly journals Reality and Super-Reality: Properties of a Mathematical Multiverse

Axiomathes ◽  
2019 ◽  
Vol 30 (4) ◽  
pp. 453-478
Author(s):  
Alan McKenzie
Keyword(s):  
Quantum Theory ◽  
Mathematical Structure ◽  
Self Awareness ◽  
Complete Structure ◽  
Mathematical Structures ◽  
Structural Environment ◽  
Parallel Universes ◽  
Definition Of ◽  
Rudimentary Form ◽  
The Universe

Abstract Ever since its foundations were laid nearly a century ago, quantum theory has provoked questions about the very nature of reality. We address these questions by considering the universe—and the multiverse—fundamentally as complex patterns, or mathematical structures. Basic mathematical structures can be expressed more simply in terms of emergent parameters. Even simple mathematical structures can interact within their own structural environment, in a rudimentary form of self-awareness, which suggests a definition of reality in a mathematical structure as simply the complete structure. The absolute randomness of quantum outcomes is most satisfactorily explained by a multiverse of discrete, parallel universes. Some of these have to be identical to each other, but that introduces a dilemma, because each mathematical structure must be unique. The resolution is that the parallel universes must be embedded within a mathematical structure—the multiverse—which allows universes to be identical within themselves, but nevertheless distinct, as determined by their position in the structure. The multiverse needs more emergent parameters than our universe and so it can be considered to be a superstructure. Correspondingly, its reality can be called a super-reality. While every universe in the multiverse is part of the super-reality, the complete super-reality is forever beyond the horizon of any of its component universes.

Research based on scientific realism should not make preliminary assumptions about mathematical structure representing human behavior: Cronbach and Gleser’s measure as an example

2021 ◽  
Vol 31 (3) ◽  
pp. 465-470
Author(s):  
Václav Linkov
Keyword(s):  
Human Behavior ◽  
Scientific Realism ◽  
Mathematical Structure ◽  
Mathematical Structures ◽  
Psychological Profiles ◽  
Realist Position ◽  
The World ◽  
Full Knowledge

Phenomena in the world we study can often be described by various mathematical structures. If a psychologist who studies human behavior takes a realist position, they should not choose a mathematical structure that represents this behavior without examination as to whether the phenomenon could be represented by this structure, but they should eventually choose the mathematical structure after thorough reasoning based on full knowledge of the problem. Using Cronbach and Gleser’s measure for assessing the similarities between psychological profiles, I show that psychologists often simply copy the mathematical structure used in other research without thoroughly reasoning about the problem. As Arocha (2021) shows, researchers should prefer approaches that include no unjustified assumptions about the mathematical structure that represents the behavior.

scholarly journals Image-based personalization of computational models for predicting response of high-grade glioma to chemoradiation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
David A. Hormuth ◽  
Karine A. Al Feghali ◽  
Andrew M. Elliott ◽  
Thomas E. Yankeelov ◽  
Caroline Chung
Keyword(s):  
Mathematical Models ◽  
Computational Models ◽  
Tumor Response ◽  
Treatment Resistance ◽  
High Grade Glioma ◽  
Information Criteria ◽  
Patient Specific ◽  
Model Parameters ◽  
High Grade ◽  
High Grade Gliomas

AbstractHigh-grade gliomas are an aggressive and invasive malignancy which are susceptible to treatment resistance due to heterogeneity in intratumoral properties such as cell proliferation and density and perfusion. Non-invasive imaging approaches can measure these properties, which can then be used to calibrate patient-specific mathematical models of tumor growth and response. We employed multiparametric magnetic resonance imaging (MRI) to identify tumor extent (via contrast-enhanced T1-weighted, and T2-FLAIR) and capture intratumoral heterogeneity in cell density (via diffusion-weighted imaging) to calibrate a family of mathematical models of chemoradiation response in nine patients with unresected or partially resected disease. The calibrated model parameters were used to forecast spatially-mapped individual tumor response at future imaging visits. We then employed the Akaike information criteria to select the most parsimonious member from the family, a novel two-species model describing the enhancing and non-enhancing components of the tumor. Using this model, we achieved low error in predictions of the enhancing volume (median: − 2.5%, interquartile range: 10.0%) and a strong correlation in total cell count (Kendall correlation coefficient 0.79) at 3-months post-treatment. These preliminary results demonstrate the plausibility of using multiparametric MRI data to inform spatially-informative, biologically-based predictive models of tumor response in the setting of clinical high-grade gliomas.

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