Colloquium

Can computers compose beautiful emotional music or in the style of the greats? Can a sonification of a mathematical algorithm, text or a painting sound like music that people would love to hear? How expressive can be a musical instrument that is based on a mathematical sound engine and has a touchscreen interface?

A polyiamond is an edge-connected set of cells on the triangular lattice. The size of a polyiamond is simply the number of cells it contains. The growth constant of polyiamonds, $\lambda_T$, is the limit of the ratio between the number of polyiamonds of size $n+1$ and the number of
polyiamonds of size $n$, as $n$ tends to infinity.

In this talk I will show improved lower and upper bounds on $\lambda_t$, proving that it is between 2.8424 and 3.6050.

Joint work with my Ph.D. student Mira Shalah.

Our research aims to formalize the conceptual notion of privacy.

We think of a privacy-jeopardizing-mechanism as a process of signal publication according to probability distribution which is determined by the value of a secret. Consider any two privacy-jeopardizing-mechanisms: it is natural to ask which mechanism is preferable in the context of privacy. We follow a Decision Theory flavored approach and capture the natural preference in such situations by listing some ordinal axioms. These axioms apply a preference relation model. We prove that the common f-divergence represents this relation.

We also follow the reverse direction of the axiomatization approach in order to characterize differential-privacy, which is an ad-hoc standard in Computer Science literature. The preference relation model, which is represented by differential-privacy, demonstrates some properties which are not natural in our eyes.

Our study leads to recommendation on measuring privacy loss by f-divergence functions, such as KL-divergence or Hellinger-distance.

Joint work with Prof. Rann Smorodinsky and Prof. Kobbi Nissim.

Mobile devices have become ubiquitous over the last decade, changing the way we interact with technology and with one another. Mobile devices were at first personal devices carried in our hands or pockets. They are now changing form to fit our lifestyles and an increasingly demanding amount and diversity of information to display. My research focuses on the design, development, and evaluation of novel interaction techniques with mobile devices using a human-centered approach.

Modern information networks often require maintaining multiple copies of the same data items for the purpose of coping with failures, robustness to errors, and fast access. The traditional approach for the design of data multiplication protocols relies on replication. A more recent powerful tool that facilitates low storage costs, as well as low communication costs, is erasure codes that transform a message of k symbols into a code-word with n symbols such that the original message can be recovered from a subset of the n symbols.

A major theme in current bioinformatics deals with the computational analysis of biological data produced by modern high-throughput measurement technologies. These technologies enable the examination of a tissue sample from different biological aspects. Each technology produces high-resolution profile composed of hundreds to thousands of features that describe that sample on a certain biological level.

Modern molecular biology measurement techniques such as microarrays, sequencing and mass-spectrometry produce large amounts of data and are often applied to large sets of samples. To interpret these data scientists apply statistics and data mining techniques that are tuned to identify certain structures in the data and to assess their statistical significance. Personalized medicine is largely driven by findings that stem from a combination of high throughput measurement and effective data analysis.

System synthesis refers to the task of automatically generating an executable component of a system (e.g. a software or hardware component) from a specification of the component's behavior. The traditional formalization of the problem assumes the specification is given by a logical formalism. The computational problem is typically intractable. Recent trends to system synthesis relax the problem definition and consider a variety of inputs including logical requirements, incomplete programs, and examples behaviors.

In this talk I will give an overview of several different aspects of the "local-to-global phenomena" in large combinatorial objects. Such phenomena occur naturally in many contexts in computer science, including property testing, sublinear time algorithms, coding theory, probabilistically checkable proofs, hardness of approximations, big data, and more.

Stochastic analysis of real-world signals consists of 3 main parts: mathematical representation; probabilistic modeling; statistical inference. For it to be effective, we need mathematically-principled and practical computational tools that take into consideration not only each of these components by itself but also their interplay.