Content:

In this talk, the Janashia-Lagvilava method of matrix spectral factorization [1], [2] will be described. The connection of the method with compactly supported wavelet matrices will be emphasized. Some applications of the proposed algorithm, including the resent developments in analyzing com-plex networks [3], will be discussed.

[1] L. Ephremidze, F. Saied, and I. M. Spitkovsky, “On the algorithmization of Janashia-Lagvilava matrix spectral factorization method”, IEEE Trans. Inform. Theory 64 (2018), no. 2, 728-737
[2] G. Janashia, E. Lagvilava, and L. Ephremidze, “A new method of matrix spectral factorization”, IEEE Trans. Inform. Theory 57 (2011), no. 4, 2318-2326
[3] J. N. MacLaurin and P. A. Robinson, “Determination of effective brain connectivity from activity correla-tions”, Physical Review, E 99 (2019), 042404

Biography
Lasha Ephremidze is a Research Associate at NYUAD (New York University Abu Dhabi) and Senior Scientific Researcher at the Razmadze Mathematical Institute, Tbilisi, Georgia. He received M.Sc. degree in Mathemat-ics and Education from the Tbilisi State University (1987) and Ph.D. in Physics and Mathematics from the Razmadze Mathematical Institute (1993). He also received the Doctor of Science in Physics and Mathematics degree from the same institute (2003). He had a visiting position at the Prague Mathematics Institute (2000-02). He was a Matsumae International Fellow at Okayama University (2004/05) and a JSPS Postdoctoral Fel-low at Tokai University (2005-07). Since 2009, he has been an Associate Professor in the Mathematics De-partment at Tbilisi State University. His research interests are harmonic analysis and ergodic theory.

Content:

Synthetic molecular communication is a field of research that offers many interesting, interdisciplinary and challenging new research problems. Based on synthetic molecular communication, nano-devices and nanosensors can efficiently exchange control information and useful data so that complicated processes can be controlled and various challenging tasks can be performed. Possible applications include internal body health monitoring, targeted drug dosing and non-drug viral control.

In this lecture, a general overview of the fields of application of synthetic molecular communication will be given and important applications will be presented. Afterwards, physical and technical characteristics as well as differences between traditional and molecular communication systems will be shown. Afterwards, the molecular channel will be discussed and modelled for the design of the communication system. Finally, the achievable transfer rate for molecular communication is determined and discussed.

Simulation results round off the lecture.

Duration approx. 50 minutes

Abstract:

In industrial machine type communications, an increasing number of wireless devices communicate under reliability, latency, and confidentiality constraints, simultaneously. From information theory, it is known that wiretap codes can asymptotically achieve reliability (vanishing block error rate (BLER) at the legitimate receiver Bob) while also achieving secrecy (vanishing information leakage (IL) to an eavesdropper Eve). However, under finite block length, there exists a tradeoff between the BLER at Bob and the IL at Eve.

In this presentation, it is shown how neural network autoencoders can be used to flexibly design finite blocklength wiretap codes. To attain this goal, a multi-objective programming problem is formulated, which takes the BLER at Bob and the IL at Eve into account. Simulation results show that the proposed scheme can find codes outperforming polar wiretap codes with respect to both BLER and IL simultaneously.

Abstract:

The multiple-access channel (MAC) is one of the few multi-user communication systems that is completely understood. That is, if the communication medium is classical. The quantum MAC has been studied for about 20 years, starting with work by the present speaker for cq-channels, and then by Devetak/Hsieh/W. for general channels with entanglement-assistance, and others, but perhaps amazingly, we are still far away from a complete understanding.

I will review the known results and open questions about the quantum MAC, especially with a view to communication assisted by shared correlations between the communicating parties.

Abstract:

We consider the compound memoryless quantum multiple-access channel (QMAC) with two sending terminals. In this model, the transmission is governed by the memoryless extensions of a completely positive and trace preserving map which can be any element of a prescribed set of possible maps. We study a communication scenario, where one of the senders shares classical message transmission goals with the receiver while the other sends quantum information.

Combining powerful universal random coding results for classical and quantum information transmission over point-to-point channels, we establish universal codes for the mentioned two-sender task. Conversely, we prove that the two-dimensional rate region achievable with these codes is optimal. In consequence, we obtain a multi-letter characterization of the capacity region of each compound QMAC for the present transmission task.

Abstract:

The developments in modern communication systems are rapid. Especially quantum communication systems allow us to exploit new possibilities while at the same time imposing fundamental limitations. Quantum information processing systems provide huge theoretical advantages over their classical counterparts. The impact of quantum information processing systems on our daily live is nonetheless still zero, the main reason for that being the difficulty to store and manipulate quantum states in a predictable and reliable manner.

We bring these two aspects together, namely we investigate the transmission of messages from a sending to a receiving party. The messages ought to be kept secret from an eavesdropper. Communication takes place over a quantum channel which is, in addition to noise from the environment, subjected to the action of a jammer which actively manipulates the states.

Abstract:

We show how to obtain perfect samples from a quantum Gibbs state on aquantum computer. To do so, we adapt one of the “Coupling from the Past”-algorithms proposed by Propp and Wilson. The algorithm has a probabilistic run-time and produces perfect samples without any previous knowledge of the mixing time of a quantum Markov chain. To implement it, we assume we are able to perform the phase estimation algorithm for the underlying Hamiltonian and implement a quantum Markov chain that satisfies certain conditions.

We provide some examples of quantum Markov chains that satisfy these conditions and analyze the expected run-time of the algorithm, which depends strongly on the degeneracy of the underlying Hamiltonian. For Hamiltonians with highly degenerate spectrum it is efficient, as it is polylogarithmic in the dimension and linear in the mixing time. For non-degenerate spectra its runtime is essentially the same as its classical coun-terpart, which is linear in the mixing time and quadratic in the dimension, up to a logarithmic factor in the dimension.

We analyze the circuit depthnecessary to implement it, which is proportional to the sum of the depth nec-essary to implement one step of the quantum Markov chain and one phase estimation. This algorithm is stable under noise in the implementation of different steps. We also briefly discuss how to adapt different “Coupling from the Past”-algorithms to the quantum setting.

Abstract:

Randomized benchmarking is a protocol to estimate the average fidelity of noisy quantum gates efficiently by estimating how fast a semigroup of quantum channels converges. Most results in the literature only hold for Clifford gates and here we give a protocol to estimate the average gate fidelity for any set of gates that are a representation of a group. Moreover, one of the main assumptions of the randomized benchmarking protocol is that we may generate samples from the Haar measure of the group.

We relax this assumption to approximate samples and show how to implement the protocol by only performing gates that generate the group and one arbitrary group element.

Abstract:
What is the most virulent Achilles heel of modern cryptography and hardware security?  It could be argued that these are the digital secrets or keys that need to be stored permanently, but securely in hardware.  Both physical attacks and malware can potentially get hold of these keys, possibly leading to security issues. 

Physical Unclonable Functions (PUFs), which were invented at MIT more than a decade ago, have shown us that certain cryptographic tasks can be accomplished without permanently stored digital secrets in the hardware, however.  They surprisingly enable fundamental schemes like identification or tamper-sensing without classical keys.     

Our talk deals with a recent extension of this concept.  We pose the general question whether certain physical statements (such as “the temperature of a certain object O is X° Celsius”, or “a certain object O has been destroyed”, or “two objects O₁ and O₂ are at a distance D to each other”, or “a certain being/animal is alive”) can be proven over digital communication lines without using classical, permanent digital keys in the hardware of the prover.  Our question is actually answered to the affirmative, and we present protocols and proof-of-concept implementations for all four example statements above.  The corresponding schemes are called “Virtual Proofs of Reality” by us.  

Our talk builds upon a recent publication on the same topic from IEEE S&P 2015.

Short Bio:  Ulrich Rührmair is a Junior Group Leader on “Physical Cryptography and Physical Security” at the Ruhr University Bochum.  He holds an MSc from Oxford, one PhD from TU Berlin, and another PhD from TU Munich, where he has founded and for several years led the so-called physical cryptography project.  His research generally deals with physical unclonable functions, physical cryptography and physical security, as well as with complexity theory, cryptography, and security at large.  Most recently, he became interested in novel disorder-based primitives beyond PUFs:  For example SIMPL Systems, which are a public key variant of PUFs, or Virtual Proofs of Reality, which aim to prove physical statements over digital communication lines.  Ulrich has co-authored over 50 papers on the topic, and has served regularly on the program committees of leading conferences in the area, including IEEE S&P, CHES, and HOST.  He is the founder and co-organizer of the ASHES workshop at ACM CCS.

Abstract:

Early stopping of iterative algorithms is a widely-used form of regularization in statistics, commonly used in conjunction with boosting and related gradienttype algorithms. Although consistency results have been established in some settings, such estimators are less well-understood than their analogues based on penalized regularization. In this paper, for a relatively broad class of loss functions and boosting algorithms (including L2-boost, LogitBoost and AdaBoost, among others), we exhibit a direct connection between the performance of a stopped iterate and the localized Gaussian complexity of the associated function class. This connection allows us to show that local fixed point analysis of Gaussian or Rademacher complexities, now standard in the analysis of penalized estimators, can be used to derive optimal stopping rules. We derive such stopping rules in detail for various kernel classes, and illustrate the correspondence of our theory with practice for Sobolev kernel classes.

Abstract:

Machine-to-machine and human-to-machine communications are essential aspects incorporated in the framework of fifth generation wireless connectivity.

These new applications demand a strict adherence to end-to-end latency and robustness/reliability of a communication link.

The security for these applications and their necessary latency requirements must be embedded in the physical domain.
Furthermore, for many of the applications discussed, the message transmission
problem, as has been defined by Shannon, is too limiting. For this kind of communication, the receiver must be in a position to
successfully decode all the messages from the sender.

To the contrary it is the communication task of identification best depicting the communication
task in the new applications. The task of identification was introduced by R. Ahlswede and G. Dueck. In this scenario,
the receiver is asked only to decide whether the sender has sent him a relevant message or not.  Naturally, the sender has no information about which
messages the receiver considers important.  The relevance of certain messages for the receiver can be changed during the application.

We determine the identification capacity of classical and classical-quantum compound channels and arbitrarily varying channels with a wiretapper. It turns out that the secure identification capacity
formula fulfills a dichotomy theorem:
It is positive and equals the identification capacity of the channel if its message transmission secrecy capacity is positive.
Otherwise, the
capacity is zero. Furthermore, we analyze the (dis-)continuity and (super-)additivity of the capacities.

Last year marked the Claude Shannon centenary. One of his many elegant results is linked with the topic of Sampling Theory. Seen from an abstract point of view, if a given signal/function is smooth, then, the sampling theory deals with conditions under which signal reconstruction/approximation is perfect. The constraint that a given signal is bandlimited (or compactly supported in Fourier domain) is a mathematical construct that somehow measures the smoothness of a function. For bandlimited functions, this topic is well understood and goes in the name of Nyquist--Shannon Sampling theorem. In the past four decades---thanks to the wavelet revolution---considerable advancements have been made in this area which now incorporates an alternative viewpoint: sampling theory as approximation of functions and covers the case of non-bandlimited, as well as sparse signals.

The idea that Fourier transform of a function forms a cyclic group---four, consecutive Fourier transforms of a function, produces the same function again---attracted the attention of several mathematicians including Norbert Wiener. This resulted in the formalization of the fractional Fourier transform or the FrFT domain (parametrized by an additional parameter) and later, the Special Affine Fourier Transform.

In this talk, we give a first hand account of new results linked with the extension of Shannon’s Sampling theory for the Special Affine Fourier Transform or the SAFT. We will discuss a version of the convolution operator that results in multiplication of the SAFT spectrums of the signals involved. On way, will discuss approximation theory for finite energy functions that live in shift-invariant subspaces. Lastly, we will show how to can one sample and recover sparse signals in the SAFT domain. The fact that the SAFT parametrically generalizes a number of well known unitary transformations leads to a unifying framework for sampling and approximation theory. All of our results are backward compatible with the Fourier transform.

This is joint work with Ahmed I. Zayed and Yonina Eldar.

Speaker Biography:

Ayush Bhandari is a researcher at the MIT where he works in the area of computational imaging. He was previously a was a visiting researcher at INRIA--Rennes in France. From 2009--2010, he was an Associate Scientist at the Temasek Labs in Singapore where he worked on problems related to digital communications and receiver design. During the same time, he was visiting researcher at the Chinese University of Hong Kong (CUHK) and later, at the LCAV, Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland. Before moving to MIT, his last employment was at the Biomedical Imaging Group of Prof. Michael Unser at the EPFL, Switzerland.

He received the best student paper award at two IEEE conferences. He is mainly interested in the theory of optimal/efficient signal approximation, representation and its applications in digital communications. He is fond of the sampling theory, its historical roots and topics that are linked with this area.

For any given channel with classical inputs and possibly quantum outputs, quantum mechanics allows us to define a dual classical-input channel by viewing both as different parts of the same quantum channel. In this talk I will describe how the new uncertainty relations for a general class of entropies imply that the performance of a given code over a given channel is entirely characterized by the performance of the dual code on the dual channel. This has several applications. In the context of polar codes, it implies that the rates of polarization to ideal and useless channels must be identical. Duality also relates the tasks of channel coding and privacy amplification, implying that the finite blocklength performance of extractors and codes is precisely linked, and that optimal rate extractors can be transformed into capacity-achieving codes, and vice versa. Finally, duality also extends to the EXIT function of any channel and code. Here it implies that for any channel family, if the EXIT function for a fixed code has a sharp transition, then it must be such that the rate of the code equals the capacity at the transition. This may give a different route to proving a code family achieves capacity by establishing sharp EXIT function transitions.

The quantum capacity of a memoryless channel determines the maximal rate at which we can communicate reliably over asymptotically many uses of the channel. Here we illustrate that this asymptotic characterization is insufficient in practical scenarios where decoherence severely limits our ability to manipulate large quantum systems in the encoder and decoder. In practical settings, we should instead focus on the optimal trade-off between three parameters: the rate of the code, the size of the quantum devices at the encoder and decoder, and the fidelity of the transmission.

We find approximate and exact characterizations of this trade-off for various channels of interest, including dephasing, depolarizing and erasure channels. In each case, the trade-off is parameterized by the capacity and a second channel parameter, the quantum channel dispersion. In the process, we develop several bounds that are valid for general quantum channels and can be computed for small instances.

The classical kernel theorem for C_c^{\infty} and its dual space due to Laurent Schwartz in 1952 is a key result in the theory of distributions. Shortly after, by Grothendieck, nuclear spaces were invented. These spaces have very similar properties in the sense that also for those a kernel theorem is available. The Schwartz space of smooth rapidly decreasing functions is an important and widely used example of a nuclear space. The existence of a kernel theorem has always been attributed to nuclear spaces. Therefore it is very surprising that there exists a certain non-nuclear Banach space for which a kernel theorem is possible. This space is Feichtinger's algebra, and it is a special case of the so-called modulation spaces, which are widely used in, e.g., time-frequency analysis and the theory of pseudo-differential operators.

In this talk I will give an introduction to these spaces, and talk about two important variants of its kernel theorem. This is joint work with Hans Georg Feichtinger.