## Mathematical Medicine.

**Moderators:** honeev, Leonid, amiradm, BioTeam

### Mathematical Medicine.

Who is interested in the use of propositional logic for explaning some particularities of monosynapsis?

A. LUCIANO D. GRECO

Biomedicine and peace have to be like two wings of a single condor.

Biomedicine and peace have to be like two wings of a single condor.

### Re: Mathematical Medicine.

Sure.

Is an importan field. You have to think about it.

Is an importan field. You have to think about it.

A. LUCIANO D. GRECO

Biomedicine and peace have to be like two wings of a single condor.

Biomedicine and peace have to be like two wings of a single condor.

### Information.

Centre for Mathematical Medicine and Biology- http://www.maths.nott.ac.uk/research/cmmb/

Mathematical Medicine- Research Centre that will focus on research utilizing mathematics to therapeutic challenges in medicine.http://www.fields.utoronto.ca/programs/scientific/CMM/

Fields Institute - Applications of Mathematics in Medicine- http://www.fields.utoronto.ca/programs/scientific/03-04/mathmedicine/

IngentaConnect Publication: http://www.ingentaconnect.com/content/oup/imammb

Glorfindel of Gondolin: Mathematical medicine? http://www.cuivienen.org/blog/2005/10/mathematical_medicine.html

MSc in Mathematical Medicine and Biology: MRC studentships availablehttp://www.maths.nottingham.ac.uk/news/shownews.php?newsID=45

I hope this links helps to understand the importance of the present topic.

Mathematical Medicine- Research Centre that will focus on research utilizing mathematics to therapeutic challenges in medicine.http://www.fields.utoronto.ca/programs/scientific/CMM/

Fields Institute - Applications of Mathematics in Medicine- http://www.fields.utoronto.ca/programs/scientific/03-04/mathmedicine/

IngentaConnect Publication: http://www.ingentaconnect.com/content/oup/imammb

Glorfindel of Gondolin: Mathematical medicine? http://www.cuivienen.org/blog/2005/10/mathematical_medicine.html

MSc in Mathematical Medicine and Biology: MRC studentships availablehttp://www.maths.nottingham.ac.uk/news/shownews.php?newsID=45

I hope this links helps to understand the importance of the present topic.

A. LUCIANO D. GRECO

Biomedicine and peace have to be like two wings of a single condor.

Biomedicine and peace have to be like two wings of a single condor.

### Modelling

An interesting paper: http://www.saber.ula.ve/cgi-win/be_alex ... ebd=ssaber

A. LUCIANO D. GRECO

Biomedicine and peace have to be like two wings of a single condor.

Biomedicine and peace have to be like two wings of a single condor.

### Learning.

Sintaxis de la lógica del propositional. Sección 1.1.

Semántica de la lógica del propositional. Sección 1.2.

Las formas normales y terminan sistemas de conectadores. Sección 1.3.

El teorema de la compacticidad. Sección 1.5.

Sintaxis de la primera lógica de la orden. Sección 3.1.

Semántica de la primera lógica de la orden. Sección 3.2.

Satisfacción de fórmulas en estructuras. Sección 3.3.

Equivalencia universal y consecuencia semántica. Formas de Prenex. Secciones 3.4 y 3.5.1.

Introducción para modelar teoría. Sección 3.6.

Pruebas formales. Sección 4.1.

Modelos de Henkin. Los teoremas de lo completo y de la compacticidad. Sección 4.2.

Funciones recurrentes primitivas. Sección 5.1.

Funciones recurrentes. Sistemas recurrentes y recurrentemente enumerable. Breve introducción a las máquinas de Turing. Secciones 5.2.2 y 5.4.1.

(Formalization of arithmetic, Godel's theorems) Peano's axioms. Section 6.1.

Representable functions. Section 6.2.

Arithmetization of syntax. Godel numbering. Section 6.3.

Godel's first incompleteness theorem. Section 6.4.

Godel's second incompletenesss theorem. Section 6.5.

Set theory. The theories Z and ZF. Section 7.1.

Ordinal numbers. Section 7.2.

Inductive proofs and definitions. Section 7.3.

Cardinal numbers. Section 7.4.

The continuum hypothesis, large cardinals, independence results.

Semántica de la lógica del propositional. Sección 1.2.

Las formas normales y terminan sistemas de conectadores. Sección 1.3.

El teorema de la compacticidad. Sección 1.5.

Sintaxis de la primera lógica de la orden. Sección 3.1.

Semántica de la primera lógica de la orden. Sección 3.2.

Satisfacción de fórmulas en estructuras. Sección 3.3.

Equivalencia universal y consecuencia semántica. Formas de Prenex. Secciones 3.4 y 3.5.1.

Introducción para modelar teoría. Sección 3.6.

Pruebas formales. Sección 4.1.

Modelos de Henkin. Los teoremas de lo completo y de la compacticidad. Sección 4.2.

Funciones recurrentes primitivas. Sección 5.1.

Funciones recurrentes. Sistemas recurrentes y recurrentemente enumerable. Breve introducción a las máquinas de Turing. Secciones 5.2.2 y 5.4.1.

(Formalization of arithmetic, Godel's theorems) Peano's axioms. Section 6.1.

Representable functions. Section 6.2.

Arithmetization of syntax. Godel numbering. Section 6.3.

Godel's first incompleteness theorem. Section 6.4.

Godel's second incompletenesss theorem. Section 6.5.

Set theory. The theories Z and ZF. Section 7.1.

Ordinal numbers. Section 7.2.

Inductive proofs and definitions. Section 7.3.

Cardinal numbers. Section 7.4.

The continuum hypothesis, large cardinals, independence results.

A. LUCIANO D. GRECO

Biomedicine and peace have to be like two wings of a single condor.

Biomedicine and peace have to be like two wings of a single condor.

### Why?

Why mathematical medicine is not applied in a massive scale?

Wich one is the more certain answer?

1. Inexistence of political support from estates.

2. Investigators do not are informed about this interdisciplinary field of searching.

If you can, express mathematically.

Wich one is the more certain answer?

1. Inexistence of political support from estates.

2. Investigators do not are informed about this interdisciplinary field of searching.

If you can, express mathematically.

A. LUCIANO D. GRECO

Biomedicine and peace have to be like two wings of a single condor.

Biomedicine and peace have to be like two wings of a single condor.

### Re: Mathematical Medicine.

Crypt dynamics and colorectal cancer: advances in mathematical

modelling.

van Leeuwen IM, Byrne HM, Jensen OE, King JR.

Centre for Mathematical Medicine, Division of Applied Mathematics,

School of Mathematical Sciences, University of Nottingham, Nottingham

NG7 2RD, UK. [email protected]

Mathematical modelling forms a key component of systems biology,

offering insights that complement and stimulate experimental studies.

In this review, we illustrate the role of theoretical models in

elucidating the mechanisms involved in normal intestinal crypt dynamics

and colorectal cancer. We discuss a range of modelling approaches,

including models that describe cell proliferation, migration,

differentiation, crypt fission, genetic instability, APC inactivation

and tumour heterogeneity. We focus on the model assumptions,

limitations and applications, rather than on the technical details. We

also present a new stochastic model for stem-cell dynamics, which

predicts that, on average, APC inactivation occurs more quickly in the

stem-cell pool in the absence of symmetric cell division. This suggests

that natural niche succession may protect stem cells against malignant

transformation in the gut. Finally, we explain how we aim to gain

further understanding of the crypt system and of colorectal

carcinogenesis with the aid of multiscale models that cover all levels

of organization from the molecular to the whole organ.

PMID: 16671995 [PubMed - indexed for MEDLINE]

Semin Cancer Biol. 2005 Dec;15(6):494-505. Related Articles, Links Cancer, aging and the optimal tissue design. Komarova NL. Department of Mathematics, University of California, Irvine, CA 92697, USA. Division patterns or mammalian tissues, like every other feature of life, have been subject to evolutionary pressures throughout the natural history. A particular and very important design principle that we discuss in this paper is the protective role of tissue architecture against cancer. We present a stochastic dynamical model of cell renewal of epithelial tissue (colonic crypts) which explicitly includes asymmetric indefinite divisions of stem cells and symmetric, finite divisions of daughter cells. We find that the hierarchical structure of crypts plays a protective role against accumulation of double-mutants. We argue that daughter cells, and not only stem cells, can play a role in carcinogenesis. Our model also predicts the optimum number of stem cells per crypt. In most cases, higher numbers of stem cells per crypt correspond to lowering the chance of colon cancer initiation (except if mutation rates associated with daughter cells are a lot lower than those associated with stem cells). Finally, we argue that the evolutionarily optimum which corresponds to a large number of stem cells per crypt, pushes the onset of cancer to an older age, but it actually acts against older individuals by increasing their chance of developing cancer. Publication Types: Review PMID: 16143543 [PubMed - indexed for MEDLINE]

modelling.

van Leeuwen IM, Byrne HM, Jensen OE, King JR.

Centre for Mathematical Medicine, Division of Applied Mathematics,

School of Mathematical Sciences, University of Nottingham, Nottingham

NG7 2RD, UK. [email protected]

Mathematical modelling forms a key component of systems biology,

offering insights that complement and stimulate experimental studies.

In this review, we illustrate the role of theoretical models in

elucidating the mechanisms involved in normal intestinal crypt dynamics

and colorectal cancer. We discuss a range of modelling approaches,

including models that describe cell proliferation, migration,

differentiation, crypt fission, genetic instability, APC inactivation

and tumour heterogeneity. We focus on the model assumptions,

limitations and applications, rather than on the technical details. We

also present a new stochastic model for stem-cell dynamics, which

predicts that, on average, APC inactivation occurs more quickly in the

stem-cell pool in the absence of symmetric cell division. This suggests

that natural niche succession may protect stem cells against malignant

transformation in the gut. Finally, we explain how we aim to gain

further understanding of the crypt system and of colorectal

carcinogenesis with the aid of multiscale models that cover all levels

of organization from the molecular to the whole organ.

PMID: 16671995 [PubMed - indexed for MEDLINE]

Semin Cancer Biol. 2005 Dec;15(6):494-505. Related Articles, Links Cancer, aging and the optimal tissue design. Komarova NL. Department of Mathematics, University of California, Irvine, CA 92697, USA. Division patterns or mammalian tissues, like every other feature of life, have been subject to evolutionary pressures throughout the natural history. A particular and very important design principle that we discuss in this paper is the protective role of tissue architecture against cancer. We present a stochastic dynamical model of cell renewal of epithelial tissue (colonic crypts) which explicitly includes asymmetric indefinite divisions of stem cells and symmetric, finite divisions of daughter cells. We find that the hierarchical structure of crypts plays a protective role against accumulation of double-mutants. We argue that daughter cells, and not only stem cells, can play a role in carcinogenesis. Our model also predicts the optimum number of stem cells per crypt. In most cases, higher numbers of stem cells per crypt correspond to lowering the chance of colon cancer initiation (except if mutation rates associated with daughter cells are a lot lower than those associated with stem cells). Finally, we argue that the evolutionarily optimum which corresponds to a large number of stem cells per crypt, pushes the onset of cancer to an older age, but it actually acts against older individuals by increasing their chance of developing cancer. Publication Types: Review PMID: 16143543 [PubMed - indexed for MEDLINE]

A. LUCIANO D. GRECO

Biomedicine and peace have to be like two wings of a single condor.

Biomedicine and peace have to be like two wings of a single condor.

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