לוח שנה משולב

Periodic Jacobi matrices on the line have a very rich spectral theory, one of whose ingredients is the Floquet theory of eigenfunctions. In this talk we will discuss ongoing work that attempts to generalize this theory to more general trees. We will describe some results obtained in joint works with Jess Banks, Jorge Garza Vargas, Eyal Seelig and Barry Simon.

Statistical physics successfully accounts for phenomena involving a large number of components using a probabilistic approach with predictions for collective properties of the system. While biological cells contain a very large number of interacting components, (proteins, RNA molecules, metabolites, etc.), the cellular network is understood as a particular, highly specific, choice of interactions shaped by evolution, and therefore difficultly amenable to a statistical physics description. Here we show that when a cell encounters an acute but non-lethal stress, its perturbed state can be modelled as random network dynamics. Strong perturbations may therefore reveal the dynamics of the underlying network that are amenable to a statistical physics description. We show that our experimental measurements of the recovery dynamics of bacteria from a strong perturbation can be described in the framework of physical aging in disordered systems (Kaplan Y. et al, Nature 2021). Further experiments on gene expression confirm predictions of the model. The predictive description of cells under and after strong perturbations should lead to new ways to fight bacterial infections, as well as the relapse of cancer after treatment.

We explore the possibility of obtaining general-purpose program obfuscation for all circuits by way of making only simple, local, functionality-preserving random perturbations in the circuit structure. Towards this goal, we use the additional structure provided by reversible circuits,  but no additional algebraic structure.


We start by formulating a new (and relatively weak) obfuscation task regarding the ability to obfuscate  random circuits of  bounded length.  We call such obfuscators  Random Input

The lecture presents recent results obtained in the laboratory of Prof. Oleg Vasyutinskii in the Ioffe Institute, St.Petersburg, Russia along several directions of application of modern laser techniques for investigation of the dynamics of molecules relevant for biology and medicine. The particular directions under discussion will be as follows.
• Investigation of energy transfer in the excited states of molecular probes in solutions by means of polarized fluorescence spectroscopy.
• Pump-and-probe polarization modulation spectroscopy for investigation of sub-picosecond dynamics in excited biomolecules.
• Dynamics of singlet oxygen generation and degradation in solutions and on organic surfaces.

: Numerous studies have identified travelling waves in the cortex and suggested they play important roles in brain processing. These waves are most often measured using macroscopic methods that do not allow assessing wave dynamics at the single neuron scale and analyzed using techniques that smear neuronal excitability boundaries. In my talk, I will present a new approach for discriminating travelling waves from modular activation. Using this approach I will show that Calcium dynamics in mouse cortex and spiking activity in turtle cortex are dominated by modular activation rather than by propagating waves. I will then show how sequentially activating two discrete brain areas can appear as travelling waves in EEG simulations and present an analytical model in which modular activation generates wave-like activity with variable directions, velocities, and spatial patterns. I will end by illustrating why a careful distinction between modular and wave excitability profiles across scales will be critical for understanding the nature of cortical computations.