6 research outputs found
Identifying parameter regions for multistationarity
Mathematical modelling has become an established tool for studying the
dynamics of biological systems. Current applications range from building models
that reproduce quantitative data to identifying systems with predefined
qualitative features, such as switching behaviour, bistability or oscillations.
Mathematically, the latter question amounts to identifying parameter values
associated with a given qualitative feature.
We introduce a procedure to partition the parameter space of a parameterized
system of ordinary differential equations into regions for which the system has
a unique or multiple equilibria. The procedure is based on the computation of
the Brouwer degree, and it creates a multivariate polynomial with parameter
depending coefficients. The signs of the coefficients determine parameter
regions with and without multistationarity. A particular strength of the
procedure is the avoidance of numerical analysis and parameter sampling.
The procedure consists of a number of steps. Each of these steps might be
addressed algorithmically using various computer programs and available
software, or manually. We demonstrate our procedure on several models of gene
transcription and cell signalling, and show that in many cases we obtain a
complete partitioning of the parameter space with respect to multistationarity.Comment: In this version the paper has been substantially rewritten and
reorganised. Theorem 1 has been reformulated and Corollary 1 adde
Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness
Guarded Kleene Algebra with Tests (GKAT) is an efficient fragment of KAT, as it allows for almost linear decidability of equivalence. In this paper, we study the (co)algebraic properties of GKAT. Our initial focus is on the fragment that can distinguish between unsuccessful programs performing different actions, by omitting the so-called early termination axiom. We develop an operational (coalgebraic) and denotational (algebraic) semantics and show that they coincide. We then characterize the behaviors of GKAT expressions in this semantics, leading to a coequation that captures the covariety of automata corresponding to these behaviors. Finally, we prove that the axioms of the reduced fragment are sound and complete w.r.t. the semantics, and then build on this result to recover a semantics that is sound and complete w.r.t. the full set of axioms
Guarded Kleene Algebra with Tests: Coequations, Coinduction, and Completeness
Guarded Kleene Algebra with Tests (GKAT) is an efficient fragment of KAT, as it allows for almost linear decidability of equivalence. In this paper, we study the (co)algebraic properties of GKAT. Our initial focus is on the fragment that can distinguish between unsuccessful programs performing different actions, by omitting the so-called early termination axiom. We develop an operational (coalgebraic) and denotational (algebraic) semantics and show that they coincide. We then characterize the behaviors of GKAT expressions in this semantics, leading to a coequation that captures the covariety of automata corresponding to these behaviors. Finally, we prove that the axioms of the reduced fragment are sound and complete w.r.t. the semantics, and then build on this result to recover a semantics that is sound and complete w.r.t. the full set of axioms
On slope genera of knotted tori in 4-space
In this note, we investigate genera for the slopes of a knotted torus in the
4-sphere analogous to the genus of a classical knot. We compare various
formulations of this notion, and use this notion to study the extendable
subgroup of the mapping class group of the knotted torus.Comment: 24 pages, accepted for publication by Pacific Journal of Mathematic
Joint Forest Planning and Management (JFPM) in the Eastern Plains Region of Karnataka: A Rapid Assessment
Over the past decade Joint Forest Management (JFM) has become the key concept through which forest generation activities are being implemented in most parts of India. This study was a rapid independent assessment of the JFPM activities conducted by Karnataka Forest department under a massive loan from the Japanese Bank for International Co-operation, focusing on the northern and southern maidan regions. The assessment used data from various sources at different scales and depth, including macro-level data gathered by the department itself, responses to a mail-in questionnaire, observations from brief field visits to a number of villages, and from in-depth case studies in a few villages. The study uncovered several lacunae in the way JFPM was being undertaken. Many of the basic tenets of ‘joint planning and management’ like consultation with villagers and setting up of Village Forest Committees (VFCs) are being violated from the outset. The selection of villages has been poor. Most VFCs exist in name only with poor participation of the village general body.Some of the lacunae in JFPM implementation are due to lacunae in the basic framework for JFPM. It is also true that the Eastern Plains region presents special challenges to JFPM implementation. But genuine JFPM is generally absent even in pockets where favourable conditions exist. On the contrary, the few ‘success’ stories are often cases of exploiting existing hierarchies to meet narrowly defined goals. Thus, the major cause of the poor quality of JFPM processes and outcomes is the refusal of the implementation agency to seriously commit itself to the concept of participatory, people-oriented forestry
Identifying parameter regions for multistationarity
<div><p>Mathematical modelling has become an established tool for studying the dynamics of biological systems. Current applications range from building models that reproduce quantitative data to identifying systems with predefined qualitative features, such as switching behaviour, bistability or oscillations. Mathematically, the latter question amounts to identifying parameter values associated with a given qualitative feature. We introduce a procedure to partition the parameter space of a parameterized system of ordinary differential equations into regions for which the system has a unique or multiple equilibria. The procedure is based on the computation of the Brouwer degree, and it creates a multivariate polynomial with parameter depending coefficients. The signs of the coefficients determine parameter regions with and without multistationarity. A particular strength of the procedure is the avoidance of numerical analysis and parameter sampling. The procedure consists of a number of steps. Each of these steps might be addressed algorithmically using various computer programs and available software, or manually. We demonstrate our procedure on several models of gene transcription and cell signalling, and show that in many cases we obtain a complete partitioning of the parameter space with respect to multistationarity.</p></div