In this seminar, we present a fast fully homomorphic encryption (FHE) based on GSW and its ring variants. The cryptosystem relies on the hardness of lattice problems in the unique domain (e.g. the LWE family). After a brief presentation of these lattice problems, with a few notes on their asymptotic and practical average case hardness, we will present our homomorphic cryptosystem TFHE, based on a ring variant of GSW. TFHE can operate in two modes: The first one is a leveled homomorphic mode, which has the ability to evaluate deterministic automata (or branching programs) at a rate of 1 transition every 50microseconds. For the second mode, we also show that this scheme can evaluate its own decryption in only 20milliseconds, improving on the the construction by Ducas-Micciancio, and of Brakerski-Perlman. This makes the scheme fully homomorphic by Gentry's bootstrapping principle, and for instance, suitable for representing fully dynamic encrypted databases in the cloud.

Tim Harford, Financial Times columnist and presenter of Radio 4's "More or Less", argues that politicians, businesses and even charities have been poisoning the value of statistics and data. Tim will argue that we need to defend the value of good data in public discourse, and will suggest how to lead the defence of statistical truth-telling.

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In the ongoing programme to classify noncommutative projective surfaces (connected graded noetherian domains of Gelfand-Kirillov dimension three) a natural question is:  what are the minimal models within a birational class?  It is not even clear a priori what the correct definition is of a minimal model in this context.

We show that a generic Sklyanin algebra (a noncommutative analogue of P^2) satisfies the surprising property that it has no birational connected graded noetherian overrings, and explain why this is a reasonable definition of 'minimal model.' We show also that the noncommutative versions of P^1xP^1 and of the Hirzebruch surface F_2 are minimal.
This is joint work in progress with Dan Rogalski and Toby Stafford.

 

We consider the Cauchy (or steepest descent) method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this worst-case behavior is exhibited by a certain convex quadratic function. We also give worst-case complexity bound for a noisy variant of gradient descent method. Finally, we show that these results may be applied to study the worst-case performance of Newton's method for the minimization of self-concordant functions.

The proofs are computer-assisted, and rely on the resolution of semidefinite programming performance estimation problems as introduced in the paper [Y. Drori and M. Teboulle.  Performance of first-order methods for smooth convex minimization: a novel approach. Mathematical Programming, 145(1-2):451-482, 2014].

Joint work with F. Glineur and A.B. Taylor.

Soft active materials are largely employed to realize devices (actuators), where deformations and displacements are triggered by a wide range of external stimuli such as electric field, pH, temperature, and solvent absorption. The effectiveness of these actuators critically depends on the capability of achieving prescribed changes in their shape and size and on the rate of changes. In particular, in gel–based actuators, the shape of the structures can be related to the spatial distribution of the solvent inside the gel, to the magnitude and the rate of solvent uptake.

In the talk, I am going to discuss some results obtained by my group regarding surface patterns arising in the transient dynamics of swelling gels [1,2], based on the stress diffusion model we presented a few years ago [3]. I am also going to show our extended stress diffusion model suited for investigating swelling processes in fiber gels, and to discuss shape formation issues in presence of fiber gels [4-6].

[1]   A. Lucantonio, M. Rochè, PN, H.A. Stone. Buckling dynamics of a solvent-stimulated stretched elastomeric sheet. Soft Matter 10, 2014.

[2]   M. Curatolo, PN, E. Puntel, L. Teresi. Full computational analysis of transient surface patterns in swelling hydrogels. Submitted, 2017.

[3]   A. Lucantonio, PN, L. Teresi. Transient analysis of swelling-induced large deformations in polymer gels. JMPS 61, 2013.

[4]   PN, M. Pezzulla, L. Teresi. Anisotropic swelling of thin gel sheets. Soft Matter 11, 2015.

[5]   PN, M. Pezzulla, L. Teresi. Steady and transient analysis of anisotropic swelling in fibered gels. JAP 118, 2015.

[6]   PN, L. Teresi. Actuation performances of anisotropic gels. JAP 120, 2016.

Bubble Dynamics

We shall discuss certain generalisations of the Rayleigh Plesset equation for bubble dynamics

Self-assembly of a filament by curvature-inducing proteins

We explore a simplified macroscopic model of membrane shaping by means of curvature-sensing proteins. Equations describing the interplay between the shape of a freely floating filament in a fluid and the adhesion kinetics of proteins are derived from mechanical principles. The constant curvature solutions that arise from this system are studied using weakly nonlinear analysis. We show that the stability of the filament’s shape is completely characterized by the parameters associated with protein recruitment and establish that in the bistable regime, proteins aggregate on the filament forming regions of high and low curvatures. This pattern formation is then followed by phase-coarsening that resolves on a time-scale dependent on protein diffusion and drift across the filament, which contend to smooth and maintain the pattern respectively. The model is generalized for multiple species of proteins and we show that the stability of the assembled shape is determined by a competition between proteins attaching on opposing sides.

In recent years, ideas from the world of partial differential equations (PDEs) have found their way into the arena of graph and network problems. In this talk I will discuss how techniques based on nonlinear PDE models, such as the Allen-Cahn equation and the Merriman-Bence-Osher threshold dynamics scheme can be used to (approximately) detect particular structures in graphs, such as densely connected subgraphs (clustering and classification, minimum cuts) and bipartite subgraphs (maximum cuts). Such techniques not only often lead to fast algorithms that can be applied to large networks, but also pose interesting theoretical questions about the relationships between the graph models and their continuum counterparts, and about connections between the different graph models.