·
**Saturday
January 9, 2016, 1:00 p.m.-5:40 p.m.**

Room 602, Washington State
Convention Center

Organizers:

**James Lynch**, Clarkson University jlynch@clarkson.edu

**Leo Marcus**, Santa Monica, CA leomarcus2@gmail.com

o 1:00 p.m.

*Many-sorted first-order model theory
as a conceptual framework for complex dynamical systems.*

**Solomon Feferman**, Stanford University

When complex biological systems (among others) are
conceived reductively, they are modeled in set-theoretical hierarchical terms
from the bottom up. But the point of view of Systems Biology (SB) is to deal
with such systems from the top down. So in this talk I will suggest the use of
many-sorted first-order structures with downward nested sorts as an alternative
conceptual framework for modeling them. In particular, the notion of a nested
substructure allows one to study parts of a structure in isolation from the
rest, while the notion of restriction allows one to study a structure relative
to some of its parts treated as black boxes. The temporal dimension can be
incorporated both as an additional sort and in the indexing of sorts, allowing
for both static and dynamic views of a system. Furthermore, one may make use of
a quite general theory of recursion on many-sorted first-order structures that
includes both discrete and continuous computation. Some possible applications
of this model-theoretic approach to SB include excision or substitution of a
part as operations on structures, similarity of biological systems via similarity
notions for structures, and homeostasis via fixed point recursion.

*Many-sorted
first-order model theory as a conceptual framework for biological and other
complex dynamical systems (draft)*

o 2:00 p.m.

*Neural Algebra and Modelling.*

**Erwin Engeler**, ETH Zurich

The mathematical model introduced in this paper attempts to explain
how complex scripts of behavior and conceptual contents can reside in, combine
and interact on large networks of interconnected basic actors. The approach
derives from modeling the neural structure and dynamics of the connectome of a
brain. The neurological hypothesis attributes functions of the brain to sets of
firing neurons, dynamically as sets of cascades of such firings, typically
visualized by imaging technologies. Such sets are represented as the elements
of what we call a neural algebra, and their interaction as its basic operation.
In particular we analyze the representation of perception and of control in its
various forms, distributed, hierarchical, recursive and especially reflexive
control, the latter modeling the concept of self-reflecting control. The main
thrust of this paper develops from the fact that characteristic properties of
these suggestive notions can be cast in the form of equations of the neural
algebra. Analyzing the solutions leads to a complete description of the
necessary structure of their neural correlates.

*Neural
Algebra **A
MODEL OF INTERACTING BRAIN FUNCTIONS* (Manuscript draft)

o 3:00 p.m.

*Dependence logic and biology.*

**Jouko**** A Vaananen**,
Department of Mathematics and Statistics, University of Helsinki, Finland

An essential part of science is detecting variation in
data. I will give an introduction to dependence logic (1), an approach to logic
emphasizing the detection of variation and dependences between variables. I
will discuss algorithmic and model theoretic properties of dependence logic,
and its relation to other notions of dependence e.g. dependence in biology,
model theory, computer science, quantum physics, and economics. In science it
is natural to consider probabilities of formulas rather than just the truth
values true/false. Suppose we have a set of assignments of fixed variables into
the domain of a first order structure. We call such sets teams. Semantics based
on teams is the underlying concept of dependence logic. We may ask, what is the
probability that a randomly chosen assignment in a team satisfies a given
first-order formula in the structure? The Hardy-Weinberg Theorem is an example
of such a first order property of probabilities in teams. In (2) we give axioms
for making inferences about first-order properties of probabilities, and prove
the completeness of our axioms.

o 4:00 p.m.

*Probabilistic
Boolean Networks as Models of Gene Regulatory Networks.*

**Ilya Shmulevich**, Institute for Systems Biology

I will present Probabilistic Boolean Networks (PBNs),
which are models of genetic regulatory networks that i)
incorporate rule-based dependencies between genes; ii) allow the systematic
study of global system dynamics; iii) are able to cope with uncertainty; iv)
permit the quantification of the relative influence and sensitivity of genes in
their interactions with other genes. PBNs share the appealing rule-based
properties of Boolean networks, but are robust in the face of uncertainty. The
dynamics of PBNs can be studied in the context of Markov Chains, with standard
Boolean networks being special cases. I will also discuss the relationship
between PBNs and Bayesian networks -- a family of graphical models that
explicitly represent probabilistic relationships between the variables. A major
objective is the development of computational tools for the identification of
potential targets for therapeutic intervention in diseases such as cancer. I
will describe several approaches for finding the best genes with which to
intervene in order to elicit desirable network behavior.

o 5:00 p.m.

*Datum Logic: A Formal Executable
Semantics for Experimental Evidence.*

**Carolyn L Talcott**, SRI International

Executable symbolic models of signal transduction have
been successfully used to analyze networks of biological reactions. Such models
can provide insights into how cells work, and a means to understand and predict
the effects of perturbations and mutations, key for cellular understanding of
disease and therapeutics. Pathway Logic (PL) is a formal system for
representing and reasoning with executable models of cellular processes.
Developing models requires significant expertise and time to collect, organize
and interpret experimental evidence; and to infer rules representing
hypothesized biochemical reaction that make up a signaling network. There is a
great need for tools to help automate the curation of executable models. The
problem of automatically constructing executable models from experimental
evidence has several aspects including: (1) formal representation of
experimental findings, (2) formal representation of rules as elements of
executable models, (3) extracting findings from papers, and (4) algorithms for
inferring rules from findings and for assembly of executable models. The PL
representation system is a solution for (2). Datum Logic is a solution to (1,4). We will describe the representation, and an approach to
inferring rules from datums.

*Inferring Executable Models from
Formalized Experimental Evidence *(related article)