**The cross linkage school:**

**A necessary pragmatism**

Arthur
Guyton in the preface of his Textbook of Medical Physiology,
8th edition (1991) writes, “Each time I revise this Textbook...
I think that someday physiology will become a completely mature
subject without change from year to year.” “However”, he admits,
“this always proves to be far from the truth... and only now
are we beginning to make inroads into many of its fundamental
secrets. Most importantly, within past few years many new techniques
for learning cellular and molecular physiology have become available.”
Then he adds his conviction; “Therefore, more and more can we
present principles in molecular and physical term, rather than
merely as of separate biological phenomenon." Clearly,
increasing bulk of information from cellular and molecular biology
demands for efficacious categorization and distribution of data
towards unified pattern generation. Thus, there is a necessity
for cross hybridization between biomedical sciences and science
of pattern generation. However, both biomedical sciences and
mathematics are so vast that there are specialties and sub-specialties
in them. Historically, the notions of specialization, specialist
and authority have frequently yielded the feelings of *insider*
and *outsider* making healthy cross hybridization and inter-disciplinary
interaction a difficult task, especially in the core applications.
By *core application*, we mean, the use of mathematics
to unify concepts by which a great mass of biological experimental
results can be brought into a coherent whole. This is obviously
different from *fringe *applications which include the
design of special purpose software and computer programs for
clinical and research uses like medical and research data keeping,
interpretation of data, patterning of EEG, ECG and other recordings,
calculation of radiation doses, etc. Some examples of core applications
of hybridization between mathematics and biological sciences
are given below.

The
analysis of control complex is very often an essential prerequisite
to understanding the pattern of feedback and adaptation as well
the purpose of physiological systems. It may involve linear
and nonlinear programmes. It is in this core area where linking
between mathematics and biomedical sciences call yield significant
leads. In recent times, the introduction of matrix-valued analytical
functions, based on advanced theories of interpolation has been
providing means of analysing and designing complex and flexible
control systems with multiple inputs and outputs, and with linear
and nonlinear processes involved.

The
concept of knot theory is also promising, to the life scientist.
The theory of operator was developed about five decades ago
at least partly to achieve mathematical model of quantum mechanics.
It has recently been suggested that there exists interesting
relationships between operator algebras and classification of
knots, meaning that a scheme to encode the pattern of a knot
in algebric elements is possible. In this case algebric manipulations
will correspond to physical actions on the knot. Then it will
also be possible to project a scheme in algebric terms how the
physical configurations of a knot can be changed to another
configuration, or to remove the knot. This appears highly promising
to many DNA researchers. Cellular DNA in a eukaryotic cell
remains in supercoil formation and thus forms a complex knotlike
structure. During DNA replication, however, the knot is pulled
apart with high order. The underlying mechanics is enigmatic.
Nevertheless, a strong possibility is there that the knot theory
may provide a lead in this respect very soon.

The language of fractals is attracting more and more attention
of scientists engaged in all fields including biological and
biomedical sciences. Fractal geometry is the dialect of the
fractal language, and fractal geometry is non-Euclidean, but
it describes natural shapes and forms more elegantly. It is
in fact an emerging notion that the patterns of neural network,
beating of a heart, chaotic properties of turbulence caused
from cardiovascular disorders etc. can be held in fractal dimensions
and Mandelbrot set, enabling the construction of their realistic
patterns.

A comment on the use of computers is required at this point.
No one does confuse between the science of pattern and the computer
science. Each is a highly powerful tool and is mutually interactive
but the individual power lies in different bearings. Mathematics
provides abstract modeling of natural phenomenon, and it also
provides algorithms for such models to be computerized. Computer,
on the other hand, provides opportunity for conceptualizing
an abstract mathematical pattern. For optimizing localization
and mapping strategies, linkage analysis and system dynamics
with which physiological sciences are so intricately bound,
computer is essential. However, the mathematical encoding forms
the heart of this computational realization. Consider the potentiality
of computer graphics of iterative maps or so called fractal
picture. This perhaps could not be achieved by only analytic
means if there would be no computer graphics. Computer graphics
not only involve mathematical pattern and computer algorithm,
but also their synchronized intersection with geometric presentation.
Examples of uses of computer aided modeling and mapping and
fractal pictures in the process of approaching biomedical problems
are rather widespread now. A quick survey of journals like
Science and Nature amply indicates a rapid increase of such
uses in the different fields of biomedical research, ranging
from DNA research, gene analysis, genetic engineering, protein
analysis to ecology, pharmacology and structural biology, from
neurophysiology to virology, from pathophysiology to computer-assisted
diagnosis.

Along with increasing versatility of computer, newer concepts
in statistical sciences have improved the handling and interpretation
of biomedical data. Now techniques in statistical analysis
like spatial statistics, boot-strap and jack-knife statistics
are of high potential value to be employed in life sciences.
Boot-strap statistics is an innovative method of generating
data using limited data, however, with statistical characteristics
being preserved. Jack-Knife statistics relates to boot-strap
and is used to reduce the bias by repeatedly cutting away a
part of data. It is now being suggested that this statistical
manipulation can be used in several fields of' biomedical studies
where available data sets are genuinely limited. Data may often
be of mixed nature: mixed of discrete and continuous variables,
and information is often partly parametric and partly nonparametric.
Hence classical nonparametric assumptions and computations,
though extensively in use as yet, have their own limitations.
It is now possible to use methods of nonparametric modeling
to assess statistically the data sets of mixed variables. Likewise,
the implication of spatial statistics in biomedical and life
sciences will appear wide and in-depth in short run with increasing
use of video and scanner type devices. The spatial statistics
will have implications in advanced analysis of data with spatial
characteristics and information, in the enhancement of' blurred
image and hidden pattern and in many other similar ways.

Time has now come when syngamy between biomedical sciences
and the science of pattern making is becoming a need. New waves
are urging upon the theoretical and applied biology. Undisputedly,
marriage between structure and function, patterns and properties,
mathematics and biology will make this sojourn healthier. It
is therefore, essential that we support this endeavor carefully.
In other words, Chester Hyman’s 'let us be tolerant to each
other's research' is no longer sufficient. Promotion of conscious,
organized and structured cross hybridization is to be encouraged.
To this effect, we publish in the following pages two debate
articles written by two budding scientists.