Anna Maltsev
University of Bristol
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Publication
Featured researches published by Anna Maltsev.
Journal of Mathematical Physics | 2013
Claudio Cacciapuoti; Anna Maltsev; Benjamin Schlein
Let XN be a N × N matrix whose entries are independent identically distributed complex random variables with mean zero and variance 1N. We study the asymptotic spectral distribution of the eigenvalues of the covariance matrix XN*XN for N → ∞. We prove that the empirical density of eigenvalues in an interval [E, E + η] converges to the Marchenko-Pastur law locally on the optimal scale, Nη/E≫(logN)b, and in any interval up to the hard edge, (logN)bN2≲E≤4−κ, for any κ > 0. As a consequence, we show the complete delocalization of the eigenvectors.
Probability Theory and Related Fields | 2015
Claudio Cacciapuoti; Anna Maltsev; Benjamin Schlein
We consider ensembles of Wigner matrices, whose entries are (up to the symmetry constraints) independent and identically distributed random variables. We show the convergence of the Stieltjes transform towards the Stieltjes transform of the semicircle law on optimal scales and with the optimal rate. Our bounds improve previous results, in particular from Erdős et al. (Adv Math 229(3):1435–1515, 2012; Electron J Probab 18(59):1–58, 2013), by removing the logarithmic corrections. As applications, we establish the convergence of the eigenvalue counting functions with the rate
Circulation Research | 2013
Anna Maltsev; Yael Yaniv; Michael D. Stern; Edward G. Lakatta; Victor A. Maltsev
Physical Review E | 2015
Fabio Deelan Cunden D Cunden; Anna Maltsev; Francesco Mezzadri
(\log N)/N
Proceedings of the National Academy of Sciences of the United States of America | 2017
Anna Maltsev; Victor A. Maltsev; Michael D. Stern
Journal of Mathematical Physics | 2017
Fabio Deelan Cunden D Cunden; Anna Maltsev; Francesco Mezzadri
(logN)/N and the rigidity of the eigenvalues of Wigner matrices on the same scale. These bounds improve the results of Erdős et al. (Adv Math 229(3):1435–1515, 2012; Electron J Probab 18(59):1–58, 2013), Götze and Tikhomirov (2013).
Communications in Mathematical Physics | 2018
Evans M. Harrell; Anna Maltsev
Rationale: A recent study published in Circulation Research by Gao et al used sinoatrial node (SAN)–targeted, incomplete Ncx1 knockout in mice to explore the role of the Na+/Ca2+ exchanger (NCX) in cardiac pacemaker. The authors concluded that NCX is required for increasing sinus rates, but not for maintaining resting heart rate. This conclusion was based, in part, on numeric model simulations performed by Gao et al that reproduced their experimental results of unchanged action potentials in the knockout SAN cells. The authors, however, did not simulate the NCX current (INCX), that is, the subject of the study. Objective: We extended numeric examinations to simulate INCX in their incomplete knockout SAN cells that is crucial to interpret the study results. Methods and Results: INCX and Ca2+ dynamics were simulated using different contemporary numeric models of SAN cells. We found that minimum diastolic Ca2+ levels and INCX amplitudes generated by remaining NCX molecules (only 20% of control) remained almost unchanged. Simulations using a new local Ca2+ control model indicate that these powerful compensatory mechanisms involve complex local cross-talk of Ca2+ cycling proteins and NCX. Specifically, lower NCX expression facilitates Ca2+-induced Ca2+ release and larger local Ca2+ releases that stabilize diastolic INCX. Further reduction of NCX expression results in arrhythmia and halt of automaticity. Conclusions: Remaining NCX molecules in the incomplete knockout model likely produce almost the same diastolic INCX as in wild-type cells. INCX contribution is crucially important for both basal automaticity of SAN cells and during the fight-or-flight reflex.
Biophysical Journal | 2011
Anna Maltsev; Victor A. Maltsev; Maxim Mikheev; Larissa A. Maltseva; Syevda Sirenko; Edward G. Lakatta; Michael D. Stern
We study the distribution of the mean radial displacement of charges of a two-dimensional (2D) one-component plasma in the thermodynamic limit N→∞ at finite temperature β>0. We compute explicitly the large deviation functions showing the emergence of a fourth-order phase transition as a consequence of a change of topology in the plasma distribution. This weak phase transition occurs exactly at the ground state of the plasma. These results have been compared with the integrable case (finite N) of plasma parameter βq2=2. In this case the problem can be mapped to the stationary properties of 2D Dyson Brownian particles and to a non-Hermitian matrix model.
Journal of Pharmacological Sciences | 2014
Victor A. Maltsev; Yael Yaniv; Anna Maltsev; Michael D. Stern; Edward G. Lakatta
Significance Living organisms are built on a hierarchy of levels, starting from macromolecules and clusters of molecules, to organelles, cells, and tissues, with interacting organs finally forming the entire organism. At the lowest of these levels life depends on individual molecules synchronizing their states to generate robust intracellular signals over the thermal noise. Here we approach the problem via statistical mechanics to describe quantitatively and deterministically this first emerging level of life. We discover that the synchronization that corresponds to termination of local Ca signals generated by clusters of Ca release channels is governed by the same equations as the phase transition associated with the reversal of magnetic field in a classical Ising ferromagnet. Intracellular Ca signals represent a universal mechanism of cell function. Messages carried by Ca are local, rapid, and powerful enough to be delivered over the thermal noise. A higher signal-to-noise ratio is achieved by a cooperative action of Ca release channels such as IP3 receptors or ryanodine receptors arranged in clusters (release units) containing a few to several hundred release channels. The channels synchronize their openings via Ca-induced Ca release, generating high-amplitude local Ca signals known as puffs in neurons and sparks in muscle cells. Despite the positive feedback nature of the activation, Ca signals are strictly confined in time and space by an unexplained termination mechanism. Here we show that the collective transition of release channels from an open to a closed state is identical to the phase transition associated with the reversal of magnetic field in an Ising ferromagnet. Our simple quantitative criterion closely predicts the Ca store depletion level required for spark termination for each cluster size. We further formulate exact requirements that a cluster of release channels should satisfy in any cell type for our mapping to the Ising model and the associated formula to remain valid. Thus, we describe deterministically the behavior of a system on a coarser scale (release unit) that is random on a finer scale (release channels), bridging the gap between scales. Our results provide exact mapping of a nanoscale biological signaling model to an interacting particle system in statistical physics, making the extensive mathematical apparatus available to quantitative biology.
Advances in Mathematics | 2011
Anna Maltsev; Benjamin Schlein
The work presents a proof of convergence of the density of energy levels to a Gaussian distribution for a wide class of quadratic forms of Fermi operators. This general result applies also to quadratic operators with disorder, e.g., containing random coefficients. The spacing distribution of the unfolded spectrum is investigated numerically. For generic systems, the level spacings behave as the spacings in a Poisson process. Level clustering persists in the presence of disorder.