360 research outputs found
Comparison of Perron and Floquet eigenvalues in age structured cell division cycle models
We study the growth rate of a cell population that follows an age-structured
PDE with time-periodic coefficients. Our motivation comes from the comparison
between experimental tumor growth curves in mice endowed with intact or
disrupted circadian clocks, known to exert their influence on the cell division
cycle. We compare the growth rate of the model controlled by a time-periodic
control on its coefficients with the growth rate of stationary models of the
same nature, but with averaged coefficients. We firstly derive a delay
differential equation which allows us to prove several inequalities and
equalities on the growth rates. We also discuss about the necessity to take
into account the structure of the cell division cycle for chronotherapy
modeling. Numerical simulations illustrate the results.Comment: 26 page
Circadian rhythm and cell population growth
Molecular circadian clocks, that are found in all nucleated cells of mammals,
are known to dictate rhythms of approximately 24 hours (circa diem) to many
physiological processes. This includes metabolism (e.g., temperature, hormonal
blood levels) and cell proliferation. It has been observed in tumor-bearing
laboratory rodents that a severe disruption of these physiological rhythms
results in accelerated tumor growth. The question of accurately representing
the control exerted by circadian clocks on healthy and tumour tissue
proliferation to explain this phenomenon has given rise to mathematical
developments, which we review. The main goal of these previous works was to
examine the influence of a periodic control on the cell division cycle in
physiologically structured cell populations, comparing the effects of periodic
control with no control, and of different periodic controls between them. We
state here a general convexity result that may give a theoretical justification
to the concept of cancer chronotherapeutics. Our result also leads us to
hypothesize that the above mentioned effect of disruption of circadian rhythms
on tumor growth enhancement is indirect, that, is this enhancement is likely to
result from the weakening of healthy tissue that are at work fighting tumor
growth
An inequality for the Perron and Floquet eigenvalues of monotone differential systems and age structured equations
For monotone linear differential systems with periodic coefficients, the
(first) Floquet eigenvalue measures the growth rate of the system. We define an
appropriate arithmetico-geometric time average of the coefficients for which we
can prove that the Perron eigenvalue is smaller than the Floquet eigenvalue. We
apply this method to Partial Differential Equations, and we use it for an
age-structured systems of equations for the cell cycle. This opposition between
Floquet and Perron eigenvalues models the loss of circadian rhythms by cancer
cells.Comment: 7 pages, in English, with an abridged French versio
Isomorphisms of types in the presence of higher-order references
We investigate the problem of type isomorphisms in a programming language
with higher-order references. We first recall the game-theoretic model of
higher-order references by Abramsky, Honda and McCusker. Solving an open
problem by Laurent, we show that two finitely branching arenas are isomorphic
if and only if they are geometrically the same, up to renaming of moves
(Laurent's forest isomorphism). We deduce from this an equational theory
characterizing isomorphisms of types in a finitary language with higher order
references. We show however that Laurent's conjecture does not hold on
infinitely branching arenas, yielding a non-trivial type isomorphism in the
extension of this language with natural numbers.Comment: Twenty-Sixth Annual IEEE Symposium on Logic In Computer Science (LICS
2011), Toronto : Canada (2011
Perspective on "New and Less New Opportunities For Mathematical Biology as Applied To Biological and Clinical Medicine"
International audienceAnother conception that makes applications of mathematics quite different from applications of mathematics to sole biology resides in the interventionist nature of medicine ..
Undecidability of Equality in the Free Locally Cartesian Closed Category (Extended version)
We show that a version of Martin-L\"of type theory with an extensional
identity type former I, a unit type N1 , Sigma-types, Pi-types, and a base type
is a free category with families (supporting these type formers) both in a 1-
and a 2-categorical sense. It follows that the underlying category of contexts
is a free locally cartesian closed category in a 2-categorical sense because of
a previously proved biequivalence. We show that equality in this category is
undecidable by reducing it to the undecidability of convertibility in
combinatory logic. Essentially the same construction also shows a slightly
strengthened form of the result that equality in extensional Martin-L\"of type
theory with one universe is undecidable
Thin Games with Symmetry and Concurrent Hyland-Ong Games
We build a cartesian closed category, called Cho, based on event structures.
It allows an interpretation of higher-order stateful concurrent programs that
is refined and precise: on the one hand it is conservative with respect to
standard Hyland-Ong games when interpreting purely functional programs as
innocent strategies, while on the other hand it is much more expressive. The
interpretation of programs constructs compositionally a representation of their
execution that exhibits causal dependencies and remembers the points of
non-deterministic branching.The construction is in two stages. First, we build
a compact closed category Tcg. It is a variant of Rideau and Winskel's category
CG, with the difference that games and strategies in Tcg are equipped with
symmetry to express that certain events are essentially the same. This is
analogous to the underlying category of AJM games enriching simple games with
an equivalence relations on plays. Building on this category, we construct the
cartesian closed category Cho as having as objects the standard arenas of
Hyland-Ong games, with strategies, represented by certain events structures,
playing on games with symmetry obtained as expanded forms of these arenas.To
illustrate and give an operational light on these constructions, we interpret
(a close variant of) Idealized Parallel Algol in Cho
Phenotype divergence and cooperation in isogenic multicellularity and in cancer
We discuss the mathematical modelling of two of the main mechanisms which
pushed forward the emergence of multicellularity: phenotype divergence in cell
differentiation, and between-cell cooperation. In line with the atavistic
theory of cancer, this disease being specific of multicellular animals, we set
special emphasis on how both mechanisms appear to be reversed, however not
totally impaired, rather hijacked, in tumour cell populations. Two settings are
considered: the completely innovating, tinkering, situation of the emergence of
multicellularity in the evolution of species, which we assume to be constrained
by external pressure on the cell populations, and the completely planned-in the
body plan-situation of the physiological construction of a developing
multicellular animal from the zygote, or of bet hedging in tumours, assumed to
be of clonal formation, although the body plan is largely-but not
completely-lost in its constituting cells. We show how cancer impacts these two
settings and we sketch mathematical models for them. We present here our
contribution to the question at stake with a background from biology, from
mathematics, and from philosophy of science
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