Related papers: The case for algebraic biology: from research to e…
This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 "Algebraic effect handlers go mainstream". It is targeted roughly at the…
We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding…
Inferring dynamic biochemical networks is one of the main challenges in systems biology. Given experimental data, the objective is to identify the rules of interaction among the different entities of the network. However, the number of…
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…
In recent years, various notions of algebraic independence have emerged as a central and unifying theme in a number of areas of applied mathematics, including algebraic statistics and the rigidity theory of bar-and-joint frameworks. In each…
These lecture notes provide an informal introduction to the theory of nonnegative polynomials and sums of squares. We highlight the history and some recent developments, especially the new connections with classical (complex) algebraic…
The fields of computing and biology have begun to cross paths in new ways. In this paper a review of the current research in biological computing is presented. Fundamental concepts are introduced and these foundational elements are explored…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
Evolution algebras were introduced into Genetics to deal with the mechanism of inheritance of asexual organisms. Their distribution into isotopism classes is uniquely related with the mutation of alleles in non-Mendelian Genetics. This…
As the frontiers of biology become increasingly interdisciplinary, the physics education community has engaged in ongoing efforts to make physics classes more relevant to life sciences majors. These efforts are complicated by the many…
We find conditions on ideals of an algebra under which the algebra is dibaric. Dibaric algebras have not non-zero homomorphisms to the set of the real numbers. We introduce a concept of bq-homomorphism (which is given by two linear maps $f,…
This paper investigates the foundations of deep learning through insight of geometry, algebra and differential calculus. At is core, artificial intelligence relies on assumption that data and its intrinsic structure can be embedded into…
Recent technological advancements in data acquisition tools allowed life scientists to acquire multimodal data from different biological application domains. Broadly categorized in three types (i.e., sequences, images, and signals), these…
We establish an analogue of the fundamental theorem of algebra for polynomial matrix equations, in which the matrices-coefficients and unknown matrix are assumed to be circulant matrices.
Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their…
Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…