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I will present the results of recent experiments with ribbons made of active, "BZ gel". The ribbons "flap", i.e.,   periodically change their curvature. When confined to a liquid interface,   the ribbons periodically "surf" from the center of the container to its walls.We analyze this motion and suggest that it represents a new, generic, type of locomotion; locomotion via curvature mismatch. In the experiments, the fluid interface is curved. When the curvatures of the ribbon and the surface are different,   both the ribbon and interface are deformed, a deformation that costs energy. Gradients of this energy lead to forces and torques on the ribbon and to its motion. We solve the equation of motion and successfully compute the trajectories of the active ribbons.Our model suggests that such motion could occur in purely solid systems. Specifically, it allows a flexible sheet, which is confined to curved (flexible or rigid) surface, to propagate without applying tangential forces. The possible relevance of this model to "curvotaxis", the phenomenon in which cells propagate and orient themselves in correlation with the substrate curvature, will be discussed. students whom are interested with a personal meeting, (The registration is limited to 5 participants) ( if you are interested in personal meeting please register)https://forms.gle/vfr9a2K3fYyKfx3d7 FOR THE LATEST UPDATES AND CONTENT ON SOFT MATTER AND BIOLOGICAL PHYSICS AT THE WEIZMANN, VISIT OUR WEBSITE: https://www.biosoftweizmann.com/

I will describe a joint work with Uri Bader, Michael Glasner and Roman Sauer in which we study unitary representations of semisimple Lie Groups that are cohomological; namely, such that the continuous cohomology of the group with coefficients in these representations is non-zero. This cohomology is a topological vector space that is not necessarily Hausdorff. The maximal Hausdorff quotient of it is called the reduced cohomology.

An essential work of Vogan and Zuckerman from 84’ solves the question completely for irreducible representations. From Vogan–Zuckerman's work one can also deduce a complete description of representations that have non-zero reduced cohomology: these are precisely representations that admit irreducible cohomological representations as sub-representations.

The question that is left is hence determining unitary representations that admit non-reduced cohomology. Up until now, non-reduced cohomology was mainly studied in the first degree, where its existence is equivalent to not having Kazhdan's property (T): H^1(G,V) is non-reduced if and only if V admits almost invariant vectors (that are not actually invariant). We prove some analoge (but more complicated) results in higher degrees, and settle the question of which representations admit non-reduced cohomology in terms of the Fell topology on the unitary dual of the group.

A copy of a permutation pattern (say, 132) in a sequence of numbers is any subsequence whose values have the same relative order as in the pattern. (Say, for 132, the first element is smallest, the second is largest, and the third is in-between.)

Counting permutation patterns has a surprisingly rich set of connections and applications in ranking, statistics, combinatorics, fine-grained complexity, and parametrized complexity, especially for fixed small k. Here are three examples:
(i) Counting 4-cycles in sparse graphs is equivalent to counting 4-patterns [Dudek and Gawrychowski, 2020].
(ii) Many fundamental tests in nonparametric statistics amount to counting k-patterns for k up to 5.
(iii) The study of twin-width in parametrized complexity has originated from a breakthrough FPT algorithm of Guillemot and Marx [2013] for permutation pattern detection, which runs in linear time when k is fixed.

In this talk I will describe an algorithm for approximately counting all k-patterns for k up to 5 in near-linear time, deterministically, to within a (1+eps)-multiplicative error. This algorithm gives the first known (conditional) separation between exact and approximate counting in this domain. Interestingly, our algorithm leverages sublinear techniques from distribution testing, which to our knowledge have not been used in a pattern counting context before.

Joint work with Slobodan Mitrović (UC Davis) and Pranjal Srivastava (MIT)

A central question in measured group theory is to classify groups up to measure equivalence. In this talk, I will present an approach to measure equivalence rigidity involving the language of groupoids. This approach was introduced by Kida for mapping class groups of surfaces, building on earlier works of, notably, Furman and its seminal result on orbit equivalence rigidity for lattices in higher rank simple Lie groups. If time allows it, I will mention an ongoing project with A. Derimay and S. Gurieva aiming at studying rigidity properties of products of such lattices, a case not covered by the celebrated Monod-Shalom paper for products of negatively curved groups.

Evolutionary changes in the host-virus interactome can alter the course of infection, but which and how often interactions evolve and how this is realized at the interface residue level, remain largely unexplored. Here, we focus on viral mimicry of motifs and domains of host proteins, that allow efficient binding to host proteins by mimicking interfaces of host proteins. Our results show that in contrast to the prevailing view of rapid interface evolution between host- and viral-interacting proteins, viruses evolved to target highly conserved host proteins. The similarity between viral mimics and their host mimicked proteins limits host capacity to escape interaction with mimics, enabling efficient viral interaction with host targets through mimicry. These results have important implications for our understanding of zoonotic events where novel host-virus protein interactions may evolve and for designing new antiviral drugs targeting interface regions between host and viral proteins.

In this seminar, I will discuss several fundamental challenges and limitations associated with high-perceptual-quality image restoration methods, and propose practical restoration and compression schemes. Specifically, I will first examine deterministic image restoration algorithms and show why striving for high output quality while maintaining consistency with the input measurements inevitably leads to algorithmic instability and vulnerability to adversarial attacks. Secondly, since the perceptual quality and distortion of the reconstructions are typically at odds with each other, a key challenge in image restoration is to minimize the distortion under a constraint of perfect output quality. To address this optimization problem, I will introduce a novel algorithm that leverages a rectified flow model to approximate the optimal solution. Finally, I will present an innovative generative approach based on pre-trained diffusion models, which produces high-quality image samples along with their losslessly compressed bit-stream representations. This new generative framework seamlessly extends to a variety of tasks, including image compression, compressed image restoration, compressed image editing, and more generally, any compressed conditional generation task.

Bio:
Guy Ohayon holds a BSc in Computer Engineering from the Technion (2021) and is in the final stages of his PhD, working under the supervision of Prof. Michael Elad and Prof. Tomer Michaeli. His doctoral research focuses on the theory and practice of image restoration and compression using generative models. Guy will soon begin a postdoctoral fellowship at the Flatiron Institute (Simons Foundation) in New York City, where he will work with Prof. Eero Simoncelli.