# Alexander MozeikaKing's College London | KCL · Randall Division of Cell and Molecular Biophysics

Alexander Mozeika

PhD

## About

51

Publications

5,317

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183

Citations

Citations since 2016

## Publications

Publications (51)

We analyse the equilibrium behaviour and non-equilibrium dynamics of sparse Boolean networks with self-interactions that evolve according to synchronous Glauber dynamics. Equilibrium analysis is achieved via a novel application of the cavity method to the temperature-dependent pseudo-Hamiltonian that characterizes the equilibrium state of systems w...

We analyse the equilibrium behaviour and non-equilibrium dynamics of sparse Boolean networks with self-interactions that evolve according to synchronous Glauber dynamics. Equilibrium analysis is achieved via a novel application of the cavity method to the temperature-dependent pseudo-Hamiltonian that characterises the equilibrium state of systems w...

We study the impact of vaccination on the risk of epidemics spreading through structured networks using the cavity method of statistical physics. We relax the assumption that vaccination prevents all transmission of a disease used in previous studies, such that vaccinated nodes have a small probability of transmission. To do so, we extend the cavit...

We study the impact of vaccination on the risk of epidemics spreading through structured networks using the cavity method of statistical physics. We relax the assumption that vaccination prevents all transmission of a disease used in previous studies, such that vaccinated nodes have a small probability of transmission. To do so we extend the cavity...

Describing the anti-tumour immune response as a series of cellular kinetic reactions from known immunological mechanisms, we create a mathematical model that shows the CD4 $$^{+}$$ + /CD8 $$^{+}$$ + T-cell ratio, T-cell infiltration and the expression of MHC-I to be interacting factors in tumour elimination. Methods from dynamical systems theory an...

It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common. Most recent studies aimed at achieving this revision rely on powerful approximation techniques that call for rigorous results against which they can be tested. In this context, the simplest case of h...

Presentation for Disordered Systems group at King's College London.

We study the space of functions computed by random-layered machines, including deep neural networks and Boolean circuits. Investigating the distribution of Boolean functions computed on the recurrent and layer-dependent architectures, we find that it is the same in both models. Depending on the initial conditions and computing elements used, we cha...

It is clear that conventional statistical inference protocols need to be revised to deal correctly with the high-dimensional data that are now common.
Most recent studies aimed at achieving this revision rely on powerful approximation techniques, that call for rigorous results against which they can be be tested. In this context, the simplest case...

Describing the anti-tumour immune response as a series of cellular kinetic reactions from known immunological mechanisms, we create a mathematical model that shows the CD4 ⁺ /CD8 ⁺ T-cell ratio, T-cell infiltration and the expression of MHC-I to be interacting factors in tumour elimination. Methods from dynamical systems theory and non-equilibrium...

We study the function-space of random neural networks and Boolean circuits. Investigating the distribution of Boolean functions computed in the recurrent and feed-forward architectures, we find that it is the same in both models. We show that, depending on the initial conditions and computing elements used, the macroscopic entropy of Boolean functi...

We study the space of Boolean functions computed by random layered machines, including deep neural networks, and Boolean circuits. Investigating recurrent and layered feed-forward architectures, we find that the spaces of functions realized by both architectures are the same. We show that, depending on the initial conditions and computing elements...

Nearly all statistical inference methods were developed for the regime where the number N of data samples is much larger than the data dimension p. Inference protocols such as maximum likelihood (ML) or maximum a posteriori probability (MAP) are unreliable if p = O(N), due to overfitting. This limitation has for many disciplines with increasingly h...

Nearly all statistical inference methods were developed for the regime where the number $N$ of data samples is much larger than the data dimension $p$. Inference protocols such as maximum likelihood (ML) or maximum a posteriori probability (MAP) are unreliable if $p=O(N)$, due to overfitting. This limitation has for many disciplines with increasing...

Presentation at the Disordered Systems group seminar (King's College London) of the mathematical modelling part of the "Roles of repertoire diversity in robustness of humoral immune response" preprint by Alexander Mozeika, Franca Fraternali, Deborah Dunn-Walters and Anthony C. C. Coolen.

We use statistical mechanics to study model-based Bayesian data clustering. In this approach, each partitioning of the data into clusters is regarded as a microscopic system state, the negative data log-likelihood gives the energy of each state, and the data set realisation acts as disorder. Optimal clustering corresponds to the ground state of the...

The adaptive immune system relies on diversity of its repertoire of receptors to protect the organism from a great variety of pathogens. Since the initial repertoire is the result of random gene rearrangement, binding of receptors is not limited to pathogen-associated antigens but also includes self antigens. There is a fine balance between having...

Example of using the population dynamics clustering algorithm arXiv:1810.02627v2 on the data from two 10d Normal distributions with 0 means and random correlation matrices sampled from the Wishart distribution with identity matrix and 10d+1 degrees of freedom parameters.

The adaptive immune system relies on diversity of its repertoire of receptors to protect the organism from a great variety of pathogens. Since the initial repertoire is the result of random gene rearrangement, binding of receptors is not limited to pathogen-associated antigens but also includes self antigens. There is a fine balance between having...

Example of using the population dynamics clustering algorithm (see arXiv:1810.02627v2) to cluster the data with 3 clusters sampled from 10d isotropic Normal distributions. The (Euclidean) distance between the means is 4.74.

We use statistical mechanics to study model-based Bayesian data clustering. In this approach, each partitioning of the data into clusters is regarded as a microscopic system state, the negative data log-likelihood gives the energy of each state, and the data set realisation acts as disorder. Optimal clustering corresponds to the ground state of the...

We use statistical mechanics to study model-based Bayesian data clustering. In this approach, each partitioning of the data into clusters is regarded as a microscopic system state, the negative data log-likelihood gives the energy of each state, and the data set realisation acts as disorder. Optimal clustering corresponds to the ground state of the...

We show that model-based Bayesian clustering, the probabilistically most systematic approach to the partitioning of data, can be mapped into a statistical physics problem for a gas of particles, and as a result becomes amenable to a detailed quantitative analysis. A central role in the resulting statistical physics framework is played by an entropy...

We use statistical physics to study model-based Bayesian clustering, which is based on stochastic partitioning of data. Using mean- field theory we show that, under natural assumptions, the lowest entropy state of this model corresponds to the optimal clustering of data. The byproduct of our analysis is a simple but e ective clustering algorithm, w...

The B cell repertoire is generated in the adult bone marrow by an ordered series of gene rearrangement processes that result in massive diversity of immunoglobulin (Ig) genes and consequently an equally large number of potential specificities for antigen. As the process is essentially random, the cells exhibiting excess reactivity with self-antigen...

High-dimensional clustering of CD24hiCD38hi transitional B cells indicates heterogeneity within the transitional population with respect to IgD, CD21, and CD23 expression, illustrated as a SPADE plot. Populations numbered 1–13 have been grouped according to expression of IgM, IgD, CD21, and CD23; see Figure 6E for a tabulated summary.

We use statistical mechanical techniques to model the adaptive immune system, represented by lymphocyte networks in which B cells interact with T cells and antigen. We assume that B- and T-clones evolve in different thermal noise environments and on different timescales, and derive stationary distributions and study expansion of B clones for the ca...

Presentation for http://www1.maths.leeds.ac.uk/applied/BSI/ meeting.

Using non-equilibrium statistical mechanics approaches to analyse dynamics of focused Metropolis decoder.

In this work we use belief-propagation techniques to study the equilibrium behaviour of a minimal model for the immune system comprising interacting T and B clones. We investigate the effect of the so-called idiotypic interactions among complementary B clones on the system's activation. Our result shows that B-B interactions increase the system's r...

We study the Langevin dynamics of the adaptive immune system, modelled by a lymphocyte network in which the B cells are interacting with the T cells and antigen. We assume that B clones and T clones are evolving in different thermal noise environments and on different timescales. We derive stationary distributions and use statistical mechanics to s...

We study spin systems on Bethe lattices constructed from d-dimensional
hypercubes. Although these lattices are not tree-like, and therefore closer to
real cubic lattices than Bethe lattices or regular random graphs, one can still
use the Bethe-Peierls method to derive exact equations for the magnetization
and other thermodynamic quantities. We comp...

We study noisy computation in randomly generated k-ary Boolean formulas. We
establish bounds on the noise level above which the results of computation by
random formulas are not reliable. This bound is saturated by formulas
constructed from a single majority-like gates. We show that these gates can be
used to compute any Boolean function reliably b...

Design and simulation results of a decoder for LDPC error-correcting codes.

Thermal noise in a cellular automaton refers to a random perturbation to its
function which eventually leads this automaton to an equilibrium state
controlled by a temperature parameter. We study the 1-dimensional majority-3
cellular automaton under this model of noise. Without noise, each cell in this
automaton decides its next state by majority v...

Recently maximum pseudo-likelihood (MPL) inference method has been
successfully applied to statistical physics models with intractable
likelihoods. We use information theory to derive a relation between the
pseudo-likelihood and likelihood functions. We use this relation to show
consistency of the pseudo-likelihood method for a general model.

We develop a systematic procedure to approximate generalized free energy in
out of equilibrium stochastic systems. The procedure only requires knowledge of
the averages of macroscopic observables and uses quasi-equilibrium distribution
to this task. As an application we consider model systems in the regime of
diverging relaxation times. We find tha...

Many natural, technological and social systems are inherently not in equilibrium. We show, by detailed analysis of exemplar models, the emergence of equilibriumlike behavior in localized or nonlocalized domains within nonequilibrium Ising spin systems. Equilibrium domains are shown to emerge either abruptly or gradually depending on the system para...

Presentation for HIIT Otaniemi Seminar at Aalto University

Many natural, technological and social systems are inherently not in
equilibrium. We show, by detailed analysis of exemplar models, the emergence of
equilibrium-like behavior in localized or nonlocalized domains within
non-equilibrium systems as conjectured in some real systems. Equilibrium
domains are shown to emerge either abruptly or gradually d...

The generating functional method is employed to investigate the synchronous
dynamics of Boolean networks, providing an exact result for the system dynamics
via a set of macroscopic order parameters. The topology of the networks studied
and its constituent Boolean functions represent the system's quenched disorder
and are sampled from a given distri...

The dynamics of Boolean networks (BN) with quenched disorder and thermal
noise is studied via the generating functional method. A general formulation,
suitable for BN with any distribution of Boolean functions, is developed. It
provides exact solutions and insight into the evolution of order parameters and
properties of the stationary states, which...

We study dynamics of Boolean networks (BN) with quenched disorder and thermal noise using the generating functional method of statistical physics. Our analysis is very general and covers a large class of recurrent BNs and related models. We show that results for the Hamming distance (the difference between the states of two networks of identical to...

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the i...

Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the ga...

Computing circuits composed of noisy logical gates and their ability to
represent arbitrary Boolean functions with a given level of error are
investigated within a statistical mechanics setting. Bounds on their
performance, derived in the information theory literature for specific gates,
are straightforwardly retrieved, generalized and identified a...

We study the Glauber dynamics of Ising spin models with random bonds, on
finitely connected random graphs. We generalize a recent dynamical replica
theory with which to predict the evolution of the joint spin-field
distribution, to include random graphs with arbitrary degree distributions. The
theory is applied to Ising ferromagnets on randomly dil...

We study the stochastic dynamics of Ising spin models with random bonds, interacting on finitely connected Poissonnian random graphs. We use the dynamical replica method to derive closed dynamical equations for the joint spin-field probability distribution, and solve these within the replica symmetry ansatz. Although the theory is developed in a ge...

## Questions

Questions (7)

Dear All,

Perhaps someone could suggest me a literature on modelling of Ab-Ag interactions. I am interested in both the "macroscopic", such as molecules of different Abs interacting with molecules of Ag (chemical kinetics of multivalent ligand-receptor complexes?), and microscopic approaches.

Thank you in advance.

Alexander

Dear All,

I have the following question.

Suppose we have a system of ODEs dx/dt=f(x) for which V(x) is a Lyapunov function, i.e. dV/dt < 0 and V>=0 with V(x^*)=0, where x^* is a fixed (or equilibrium) point of ODE.

If V(x) is also a convex function of x then the gradient descent equation dx/dt=-dV/dx will gives us a "lower bound on time it takes to converge to equilibrium" for any ODE, i.e. any f(x).

## Projects

Projects (7)

Using tools from non-equilibrium statistical mechanics to study dynamics of information processing systems.

Developing a theory of high-dimensional statistical inference using analytic tools from the statistical physics of disordered systems.