- Development new screening tool for toxic chemicals, with Department of Chemistry (press-release in ScienceDaily: New approach for screening toxic chemicals mimics mammal senses)
- Efficient Visual Intelligence Technologies (with Industrial partners, supported by "Innovate UK", two KTP projects)
The project aims at developing computationally efficient methods, algorithms and tools in the area of intelligent image processing. Examples include but are not limited to efficient real-time object detection, recognition, and false positives suppression in live video streams.
- Handling missing data in large healthcare datasets, with TARN (press-release in ScienceDaily: Trauma patient deaths peak at two weeks )
- Systems Medicine: Novel Mathematical Approaches to Personalised Care in Asthma Patients with Respiratory Biomedical Research Unit/Department of Infection, Immunity & Inflammation.
- Modelling of global epigenetic changes in pneumococcus, with Department of Genetics (press-release in ScienceDaily: Breakthrough study discovers six changing faces of 'global killer' bacteria)
- Mathematical Modeling of microRNA-Mediated Mechanisms of Translation Repression and Analysis of microRNA modes of action (press-release in ScienceDaily: Mathematicians solve decade-old debate on regulation of protein production by microRNAs in cells)
- Computational diagnosis and risk evaluation for canine lymphoma with Avacta Animal Health (press-release in ScienceDaily: New hope for beloved family pets: New blood test for canine cancer)
- Direct Calculation of Solid-Liquid Interfacial Free Energy for Molecular Systems
- Mathematical Modelling of Brain, with international team from Japan and The Netherlands (University press-release: Brain Power - Breakthrough in Mathematical Modelling)
- Branching Principal Components, Principal Cubic Complexes and Topological Grammars
- Cartography of Ratings results of the Political Atlas of the World
- Correlation, Risk and Crisis, Evolution of adaptation mechanisms (press-releases in ScienceDaily: Plants and animals under stress may provide the key to better stock market predications; 'Adaptation energy' in animals: Mathematicians provide solution to 78 year old mystery)
Our study involves development of fluorescent cell-based diagnostic assay as a new approach in high-throughput screening method. This highly sensitive optical assay operates similarly to e-noses and e-tongues which combine semi-specific sensors and multivariate data analysis for monitoring biochemical processes. The optical assay consists of a mixture of environmental-sensitive fluorescent dyes and human skin cells that generate fluorescence spectra patterns distinctive for particular physico-chemical and physiological conditions. Using chemometric techniques the optical signal is processed providing qualitative information about analytical characteristics of the samples. This integrated approach has been successfully applied (with sensitivity of 93% and specificity of 97%) in assessing whether particular chemical agents are irritating or not for human skin. It has several advantages compared with traditional biochemical or biological assays and can impact the new way of high-throughput screening and understanding cell activity. It also can provide reliable and reproducible method for assessing a risk of exposing people to different harmful substances, identification active compounds in toxicity screening and safety assessment of drugs, cosmetic or their specific ingredients.
Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning
The quadratic error functionals demonstrate many weaknesses for complex data.
- The back side of the non-quadratic error functionals is cost for optimization.
- New algorithms use Piece-wise Quadratic potentials of SubQuadratic growth (PQSQ).
- The theory of PQSQ potentials is based on the notion of the cone of minorant functions, and represents a natural approximation formalism based on the application of min-plus algebra.
- PQSQ-based algorithms are as fast as the fast heuristic methods but more accurate.
- PQSQ-based algorithms are computationally efficient for regularized sparse regression
- We formalize Selye׳s ideas about adaptation energy and dynamics of adaptation.
- A hierarchy of dynamic models of adaptation is developed.
- Adaptation energy is considered as an internal coordinate on the "dominant path" in the model of adaptation.
- The optimal distribution of resources for neutralization of harmful factors is studied.
- The phenomena of "oscillating death" and "oscillating remission" are predicted.
MicroRNAs (miRNAs) are key regulators of all important biological processes, including development, differentiation, and cancer. Although remarkable progress has been made in deciphering the mechanisms used by miRNAs to regulate translation, many contradictory findings have been published that stimulate active debate in this field. Here we contribute to this discussion in three ways.
- First, based on a comprehensive analysis of the existing literature, we hypothesize a model in which all proposed mechanisms of microRNA action coexist, and where the apparent mechanism that is detected in a given experiment is determined by the relative values of the intrinsic characteristics of the target mRNAs and associated biological processes. Among several coexisting miRNA mechanisms, the one that will effectively be measurable is that which acts on or changes the sensitive parameters of the translation process.
- Second, we have created a mathematical model that combines nine known mechanisms of miRNA action and estimated the model parameters from the literature.
- Third, based on the mathematical modeling, we have developed a computational tool for discriminating among different possible individual mechanisms of miRNA action based on translation kinetics data that can be experimentally measured (kinetic signatures).
- Acute phase proteins, C-Reactive Protein and Haptoglobin, are used for the canine lymphoma blood test.
- This test can be used for diagnostics, screening, and for remission monitoring.
- We compare various decision trees, KNN (and advanced KNN) and algorithms for probability density evaluation.
- For the differential diagnosis the best solution gives the sensitivity 83.5% and specificity 77%.
Mathematics explains puzzles of icy dust in the outer space
One of the most impressive discoveries of the Cassini spacecraft was the cryo-volcanic activity of the icy Saturnian satellite Enceladus. Water vapour and tiny ice particles, ejected from geyser like sources, form a spectacular plume that towers over the south pole of the moon up to hundreds of kilometers. The icy particles (dust), which make the visible part of the plume, are the main source of Saturn's E ring.
However, the physical process of grain formation is not understood to date. Recent work by Dr Nikolay Brilliantov and colleagues present a new quantitative mathematical model, which basically explains the observed properties of the plume. The core of the model is subsurface condensation of ice grains in the vapour. The gas is produced at depth and escapes to vacuum through cracks in the ice shell at the south pole of the moon.
The model reproduces well all the available data obtained by Cassini. The results favor conditions of liquid water near Enceladus' surface, implying an 'underground' ocean which may be a habitat for life.
- The results are published in Nature, vol. 451, p.685 (2008)
- Press Release in The New York Times
- Press Release in Astronomy
- Press Release in Science Daily
Most Accessed Paper in BMC Systems Biology in November 2008
- A Radulescu, A Gorban, A Zinovyev and A Lilienbaum. Robust Simplifications of Multiscale Biochemical Networks. BMC Systems Biology 2008, 2:86, doi:10.1186/1752-0509-2-86
- (total download ratings in November 2008)
Cellular processes such as metabolism, decision making in development and differentiation, signalling, etc., can be modeled as large networks of biochemical reactions.
In order to understand the functioning of these systems, there is a strong need for general model reduction techniques allowing to simplify models without loosing their main properties. In systems biology we also need to compare models or to couple them as parts of larger models. In these situations reduction to a common level of complexity is needed.
We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as 'pseudo-monomolecular' subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalised theory of the limiting step.
Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model.
The methods are demonstrated for simple examples and for a more complex model of NF-κB pathway. Our approach allows critical parameter identification and produces hierarchies of models. Hierarchical modeling is important in 'middle-out' approaches when there is need to zoom in and out several levels of complexity. Critical parameter identification is an important issue in systems biology with potential applications to biological control and therapeutics. Our approach also deals naturally with the presence of multiple time scales, which is a general property of systems biology models.