PhysDIS Workshop

15 May 2008, 09:00 → 17 May 2008, 18:00 Europe/Stockholm

FB42 (<a href="http://www.albanova.se/">AlbaNova</a>)

Erik Aurell, Mikko Alava

Context

The workshop is organized within the framework of the one-month Nordita program running in the month of May 2008, with additional support from the KTH ACCESS Linnaeus Center . The workshop will take place at the premises of NORDITA in Stockholm, Sweden.

Content and scope

Statistical physics has recently applied been to understanding, analysis and design of large distributed information systems. These range from decoding algorithms (Belief Propagation) and phase transitions and typical-case hardness in combinatorial optimization problems to content distribution and dynamical phenomena on the Internet, to the modelling of distributed agent systems - Peer-to-Peer networks, auction mechanisms and more.

Format and practicalities

Registration for the PhysDIS workshop is separate from registration/application for the longer PhysDIS program. There are grants for Nordic participants, the deadline for application is February 29th, 2008.

Confirmed participants include

Danny Bickson, HUJI, Israel
Magnus Boman, KTH, Sweden
Axel Brandenburg, NORDITA, Sweden
Mads Dam, KTH, Sweden
György Dan, KTH, Sweden
Neil Gershenfeld, MIT
Meesoon Ha, KAIST, South Korea
Seif Haridi, SICS and KTH, Sweden
Alex Hartmann, Osnabruck, Germany
Petter Holme, KTH, Sweden
Chin-Kun Hu, Academia Sinica, Taipei, Taiwan
Johan Håstad, KTH, Sweden (Saturday May 17)
John Hertz, NORDITA, Sweden
Karl Johansson, KTH, Sweden
Petteri Kaski, HIIT, Finland
Scott Kirkpatrick, MIT, MA and HUJI, Israel
Supriya Krishnamurthy, SICS and KTH, Sweden
Joachim Krug, Cologne, Germany
Florent Krzakala, Paris, France
Luis Lafuente, MIT, MA
Satya Majumdar, Orsay, France
Mats Nordahl, Stockholm
Paolo Muratore-Ginanneschi, Helsinki, Fínland
Pekka Orponen, TKK, Finland
Luca Peliti, Naples, Italy
Federico Ricci-Tersenghi, Rome, Italy
Heiko Rieger, Saarbrucken, Germany
Bart Selman, Cornell, NY
Jeremy Stribling, MIT, MA
Olav Tirkkonen, TKK and Nokia, Finland
Massimo Vergassola, Pasteur, France
Bing-Hong Wang, Hefei, China
Haijun Zhou, Chinese Academy of Sciences, Beijing, China
Riccardo Zecchina, Torino, Italy
Lenka Zdeborova, Orsay, France

Previous meetings in this series

This NORDITA workshop follows upon a 2007 Statphys 23 satellite meeting, for which the program and list of attendees is available, and further a planned 2008 Kavli Institute of Theoretical Physics China (KITPC, Beijing, China) event CDInfos0803, for which the registration closed July 15, 2007.

Thursday, 15 May

09:00 → 18:00 May 15

09:00 Opening of the workshop

Speakers: Prof. Erik Aurell (KTH), Mikko Alava (HUT, Espoo, Finland)

09:20 Evaluating the performance of Structured Peer-to-Peer Overlays

Overlay networks are application-level networks, or networks of acquaintances, established on top of physical networks, such as the Internet. Peer-to-Peer (P2P) systems are one class of overlay networks, in which all nodes in the system are equivalent and all tasks are carried out without the presence of any central authority. Despite their relatively short history, peer-to-peer overlays are now deployed in a multitude of new and highly popular applications. There has hence been an immense amount of interest in the research community to classify and understand the performance implications of all the design choices available for the construction of such networks, keeping in mind the specific problems they face: namely very high dynamism, lack of control, arbitrary geographical location of the constituent peers and differing bandwidth capabilities. In this talk, we describe our own (physics-based) approach to thinking about these issues.

Speaker: Dr Supriya Krishnamurthy (SICS)

Slides physdis.pdf

09:40 Coffee

10:00 Statistical physics and message-passing algorithms for Steiner trees

Given an undirected graph with positive weights on the edges, the Minimum Weight Steiner Tree (MST) problem consists in finding a connected subgraph of minimum weight that contains a selected set of ``terminal'' vertices. Such construction may require the inclusion of some non-terminal nodes which are called Steiner nodes. Clearly, an optimal sub-graph must be a tree. Solving MST is a key component of many optimization problems involving real networks. Here we discuss a general technique to translate the imposed global connectivity constrain into many local ones that can be analyzed with cavity equation techniques.
This approach leads to a new optimization algorithm for MST and allows to analyze the statistical mechanics properties of MSTs on random graphs of various types.

Speaker: Prof. Riccardo Zecchina (Politecnico di Torino)

10:40 break

11:00 A minimal model to understand the onset of congested phases in information networks.

Many efforts have been devoted to characterize the onset of congestion in communication networks. Numerical simulations performed using complex routing protocols have revealed that congestion always occurs as an effect of traffic increase, but with specific features that strictly depend on the local routing scheme. (For instance, the continuous or discontinuous character of the transition from free-flow to congested regime.) To shed light on the nature of these phenomena, we propose a minimal model of routing on networks (traffic-aware random walks) that retains all the relevant macroscopic properties, and can be analytically studied in the ensembles of uncorrelated random graphs (homogeneous or scale-free). The same approach also provides a recursive method to study the phase diagram for single network realizations.

Speaker: Dr Luca Dall'Asta (Abdus Salam ICTP)

Slides DallAsta-nordita08-congestion.pdf

11:20 Towards an Optimal Separation of Space and Length in Resolution

Most state-of-the-art satisfiability algorithms today are variants of the DPLL procedure augmented with clause learning. The main bottleneck for such algorithms, other than the obvious one of time, is the amount of memory used. In the field of proof complexity, the resources of time and memory correspond to the length and space of resolution proofs. There has been a long line of research trying to understand these proof complexity measures, but while strong results have been proven on length our understanding of space has been quite poor. For instance, it has remained open whether the fact that a formula is provable in short length implies that it is also provable in small space or whether on the contrary these measures are unrelated in the sense that short proofs can be "arbitrarily complex" with respect to space.
In this talk, we present evidence that the true answer should be that the latter case holds and provide a roadmap for how such an optimal separation result could be obtained. We do this by proving a tight bound of Omega(sqrt(n)) on the space needed for so-called pebbling contradictions over pyramid graphs of size n. This yields the first polynomial lower bound on space that is not a consequence of a corresponding lower bound on width, another well-studied measure in resolution, as well as an improvement of the weak separation in (Nordström 2006) of space and width from logarithmic to polynomial.
Joint work with Johan Håstad, Royal Institute of Technology.

Speaker: Jakob Nordström (KTH)

11:40 Lunch

13:00 Simplifying Distributed Application Development using WheelFS

It is a challenge to build applications that need to share data and are distributed across hundreds or thousands of computers in a wide-area network (e.g., PlanetLab or on a Grid). In order to cope with high latency, throughput bottlenecks, and temporary failures, such applications typically implement their own storage plan or use special-purpose storage solutions (e.g., DISC, Globus, DHash, etc.). Inspired by the success of the Google File System for cluster applications, we investigate whether a general-purpose wide-area file system could simplify building distributed applications. In particular, this talk presents WheelFS, a new distributed file system that eases the development of distributed applications such as cooperative Web caches, data-intensive Grid applications, and distributed email systems. By giving applications a familiar POSIX interface, and giving them control of how the file system handles their data in the face of the challenging wide-area network, WheelFS simplifies the development of new applications and allows reuse of much existing code -- often distributed applications can be created with just a few changes to a configuration file. This talk will present the design and implementation of WheelFS, and evaluate its performance in the context of several applications.

Speaker: Jeremy Stribling (MIT CSAIL)

Slides wheelfs-physdis.pps

13:40 break

14:00 Gaussian Belief Propagation for Solving Systems of Linear Equation

The canonical linear-algebraic problem of solving a system of linear equations arises in numerous contexts in the mathematical sciences and engineering. In this talk, we introduce an efficient Gaussian belief propagation (GaBP) solver that does not involve direct matrix inversion. The iterative nature of our approach allows for a distributed message-passing implementation of the solution algorithm. We discuss the properties of the GaBP solver, including convergence, exactness, computational complexity, message-passing efficiency and its relation to classical solution methods. The attractiveness of the proposed solver, in comparison to conventional iterative solution methods, is demonstrated using numerical examples and applications, like linear detection.
The talk is based on a joint work with Prof. Jack K. Wolf (UCSD), Prof. Paul H. Siegel (UCSD), Dr. Ori Shental (UCSD) and Prof. Danny Dolev (HUJI).

Speaker: Danny Bickson (The Hebrew University of Jerusalem)

Slides Ori_Talk_AI.pdf

14:20 Consensus under bounded connectivity control laws and time delayed communication

Multi-agent consensus problems where agents aim to attain a common value of some quantity under limited communication have received increasing attention recently, due to their application in multi-vehicle and multi-robot systems, as well as distributed estimation and filtering in networked systems. In this talk we present two recent results on consensus problems. The first part of the talk involves a control algorithm for connectivity maintenance in consensus networks with bounded inputs. In the second part, we assume that each agent receives instantaneously its own output information but receives the information from its neighbors after a constant delay and provide a theoretical analysis on the resulting equilibria.
The results are supported through numerical simulations

Speaker: Dr Dimos Dimarogonas (KTH)

Slides Alba_Nova_Workshop.ppt

14:40 Coffee

15:00 Finite size scaling in complex networks

A finite-size-scaling (FSS) theory is proposed for various models in complex networks. In particular, we focus on the FSS exponent, which plays a crucial role in analyzing numerical data for finite-size systems. Based on the droplet-excitation (hyperscaling) argument, we conjecture the values of the FSS exponents for the Ising model, the susceptible-infected-susceptible model, and the contact process, all of which are confirmed reasonably well in numerical simulations. Finally we discuss how those can be different in the annealed versions of networks.

Speaker: Dr Meesoon Ha (KAIST)

Slides MHA-FSS-NORDITA.pdf

15:20 Capacity analysis of collaborative wireless communication

Speaker: Prof. Olav Tirkkonen (TKK)

Slides PhysDISworkshop_Tirkkonen.pdf

15:40 break

16:00 Solving K-SAT by going slowly down

Speaker: Mikko Alava (HUT, Espoo, Finland)

Slides nt.pdf

16:20 Tail Behavior and Scaling of the Playback Delay for Overlay Multicast

A large number of peer-to-peer streaming systems has been proposed and deployed in recent years. Yet, there is no clear understanding of how these systems scale and how multi-path and multihop transmission, properties of all recent systems, affect the quality experienced by the peers. In this talk we present an analytical study that considers the relationship between delay and loss for general overlays: we study the trade-off between the playback delay and the probability of missing a packet and we derive bounds on the scalability of the systems. We use an exact model of push-based overlays to show that the bounds hold under diverse conditions: in the presence of errors, under node churn, and when using forward error correction and various retransmission schemes

Speaker: Dr György Dan (KTH)

16:40 Networks of caustics in turbulent aerosols

Speaker: Prof. Bernhard Mehlig (Chalmers University of Technology)

Slides mehlig.pdf

Friday, 16 May

09:00 → 19:40 May 16

09:00 Non-coding RNAs in bacteria

Speaker: Prof. Massimo Vergassola (Institut Pasteur)

09:40 Coffee

10:00 Computational Aspects of Random Boolean Networks

Random Boolean Networks (RBNs) were introduced by Kaufmann in 1969 in the context of gene expression and fitness landscapes. They were applied to the problems of cell differentiation, immune response, evolution, and neural networks. They have also attracted the interest of physicists due to their analogy with the disordered systems studied in statistical mechanics, such as the mean field spin glass. An RBN is a synchronous Boolean automaton. Each vertex has k predecessors, selected at random, and an associated Boolean function of k variables. Kauffman has shown that it is possible to tune the parameters of an RBN so that the network exhibits self-organized critical behavior ensuring both stability and evolutionary improvements. This talk focuses on computational aspects of RBNs. First, we give an introduction to RBNs and show how they can be used for the modeling of gene regulatory networks of living cells. Then, we describe three basic steps of the analysis of dynamical behavior of RBNs: redundancy removal, partitioning, and computation of attractors. Finally, we discuss open problems and outline prospectives of RBNs.

Speaker: Prof. Elena Dubrova (KTH)

Slides ElenaDubrova_workshop2008.ppt

10:20 Evolutionary dynamics in random fitness landscapes

The evolutionary search of a finite population in a rugged fitness or energy landscape with many local optima is a paradigmatic problem that connects evolutionary biology to the statistical physics of disordered systems and computer science. In this brief presentation I summarize the results of two recent studies which addressed different aspects of this problem. A detailed numerical investigation of evolutionary trajectories in a sequence space of finite extent revealed a hierarchy of dynamical regimes that are traversed with increasing population size, connecting the adaptive walk of a pointlike population to the deterministic quasispecies limit at extremely large population sizes [1]. In the second study the limit of infinite sequence length was employed, which leads to an analytically tractable problem closely related to the dynamics of records [2].

[1] K. Jain, J. Krug, Genetics 175, 1275 (2007).
[2] S.C. Park, J. Krug, JSTAT (2008) P04014.

Speaker: Prof. Joachim Krug (University of Cologne)

Slides rugged.pdf

10:40 break

11:00 Local-majority-rule dynamics: Influence of network structure and dynamics-driven structural evolutions

The mutual influence of structure and dynamical processes in a complex networked system is an active yet challenging research topic. In the present report we approach this problem by studying a simple model system, namely the local majority-rule (LMR) dynamics on an evolving network. We first show analytically and by computer simulation that the structure of the network can have a qualitative influence on the typical relaxation time of the LMR dynamics, and that scale-free networks with decaying exponent $\gamma$ in the tiny range of $2< \gamma <2.5$ are particularly efficient for the LMR process. Then we demonstrated that, under simple local rules of dynamics-structure feedback, the LMR dynamics can slowly drive the underlying network into a highly heterogeneous structure with high clustering coefficient and scale-free-like degree distributions. Most interestingly, a global hub emerges spontaneously in the network, which has direct interaction with a major fraction of all the other vertices of the network.

This work is done in collaboration with Reinhard Lipowsky and Zhen Shao.

References:
H. J. Zhou and R. Lipowsky, PNAS, 102 (2005), 10052-10057.
H. J. Zhou and R. Lipowsky, JSTAT, P01009 (2007).
Z. Shao and H. J. Zhou, arXiv: 0804.3181v1 (2008).

Speaker: Prof. Haijun Zhou (Chinese Academy of Sciences)

Slides LMR_evolution.ppt

11:40 Lunch

13:00 Searching for Scalable Solutions to really Large Problems: Experiments

Statistical mechanics turned a corner with Mezard and Zecchina's realization that its methods could be applied to solve individual combinatorial problems as well as to characterize the expected outcome of classes of problems. But the methods, such as message passing or simulated annealing, that stay closest to the physical analogies can be extremely time-consuming and may not scale to large engineering problems. Experience with heuristics, which work simply and fast when they work and fail miserably when they do not, suggest that problem complexity and method success have a phase structure in problems with parameters to vary. Recent attacks on decoding simple but powerful LPDC codes have called attention to the possibility of using linear programming and other powerful, scalable methods to solve problems where a unique solution is expected (or guaranteed). We have recently extended this approach with random retrial heuristics. Applying these methods to the hardest known Sudoku problems, we establish that when a unique solution is known to exist, it can be found by scalable methods with probability epsilon with a cost multiple delta(epsilon), a new way of expressing the resulting complexity of this phase.

Speaker: Prof. Scott Kirkpatrick (School of Engineering and CS, HUJI)

Slides Sudoku_Stockholm_2008.ppt

13:40 break

14:00 Searching for Scalable Solutions to really Large Problems: Theory

Linear Programming can solve some unlikely problems, like decoding parity check codes, sorting, and other things. A lovely old theorem by Birkhoff and von Neumann distinguishes the cases in which the solution is guaranteed to lie on the integers 0 and 1. Unfortunately, this result fails to apply to NP-Complete problems -- it guarantees to solve the 8 rooks problem, but not the 8 queens, and also fails to cover our Sudoku examples. We have explored a number of ways in which to cast problems as LPs. It seems to matter.

Speaker: Dr Luis Lafuente (MIT CBA)

Slides 08.05.nordita-LAFUENTE.pdf

14:20 Issues in Distributed Aggregation

Distributed aggregation is the problem of computing, in a decentralized and scalable way, global functions of local values residing at nodes in a network. Interesting aggregation functions include average, counting, sum, min/max, voting, medians and quantiles, and thresholds. In network management applications, our primary domain of interest, such aggregates can be useful indicators of the network state. The computation may be subject to constraints regarding a range of parameters such as accuracy, responsiveness, robustness to node or link failures, and security. In the talk I survey recent work at KTH on distributed aggregation both using tree-based and gossip-based approaches. A particular difficulty with gossip-based aggregation is to recover state in case of node failures. We outline a recently developed solution which is convergent under the assumption that no two neighbouring nodes fail within the same round.

Speaker: Prof. Mads Dam (KTH)

14:40 Coffee

15:00 Solving Industrial SAT Problems

Tools for solving the propositional satisfiability (SAT) problem have advanced dramatically during the last ten years and are now standardly used in industrial applications such as hardware design verification and automatic test pattern generation. SAT solvers are also becoming widely used search engines in areas with challenging computation problems such as automated planning, bioinformatics, and cryptanalysis. We discuss how a SAT solver can be used as an efficient back-end search engine in such applications. Then we review algorithmic techniques in state-of-the art solvers and novelties behind recent substantial improvements in performance for real world examples. We consider in more detail the role of branching heuristics for the performance of a SAT solver and the problem of generating computationally hard SAT instances for state-of-the-art solvers.

Speaker: Prof. Ilkka Niemelä (TKK)

15:40 break

16:00 Inferring Spike Pattern Distributions from Data

We can learn something about how large neuronal networks function from models of the spike pattern distributions constructed from data. In our work, we do this for data generated from simulated models of local cortical networks, using the approach introduced by Schneidman et al, modeling this distribution by an Ising model: P[S] = Z^{-1}exp(½Σ_{ij}J_{ij}S_iS_j+Σ_i h_i S_i). To estimate the parameters J_{ij} and h_i we use a technique based on inversion of the TAP equations. We perform the estimation procedure for subsets of the neurons of sizes N ranging from 6 up to 800 (all the excitatory neurons in the simulated network) and study the statistics of the inferred parameters. The N-dependences of both the means and the variances are well-fit, at large N, by functions of the form a/(b +N). This dependence can be accounted for in a simple way by assuming that the system is an SK spin glass in its normal phase. We verify a posteriori the assumption that it is in the normal, rather than the spin glass phase; thus, this description is self-consistent.

Speaker: Prof. John Hertz (NORDITA)

16:20 Tug-of-war of molecular motors and the role of vesicle pairing during the formation of the immunological synapse

Targeted transport of vesicles, organelles and other types of cargo is necessary for living cells to maintain their complex internal structure. Molecular motors attached to this cargo power the long-range traffic of cargo along microtubules in a bidirectional way. The attachment of two kinds of motors, one pulling towards the cell periphery and one towards the cell center, lead to a tug-of-war scenario and a cargo displacemnt distribution that depends very sensitively on microscopic details. Recently it was observed that a novel mechanism of vesicle pairing appears to be necessary for an efficient transport of perforin containing granules to the immunulogical synapse of activated cytotoxic T lymphocytes. In this short presentation we discuss the aspects of this scenario that can be understood within the framework of the tug-of-war model.

Speaker: Prof. Heiko Rieger (Universität des Saarlandes)

16:40 break

17:00 Programming Bits and Atoms

Computer Science has served to isolate programs (and programmers) from knowledge of the underlying physical mechanisms used for computation. However, in the limit in which the number of computational and physical degrees of freedom become equivalent it's no longer possible to maintain this fiction. I will explore the benefits of exposing rather than hiding the boundary between bits and atoms, including conformal computing architectures, mathematical programming models, and digital fabrication processes.

Speaker: Prof. Neil Gershenfeld (MIT CBA)

Slides 08.05.Gershenfeld.Stockholm.ppt

Saturday, 17 May

09:00 → 18:00 May 17

09:00 On the approximability of Constraints Satisfaction Problems

Speaker: Prof. Johan Håstad (KTH)

Slides slides.pdf

09:40 Coffee

10:00 Computing the Tutte polynomial in vertex-exponential time

The deletion--contraction algorithm is perhaps the most popular method for computing a host of fundamental graph invariants such as the chromatic, flow, and reliability polynomials in graph theory, the Jones polynomial of an alternating link in knot theory, and the partition functions of the models of Ising, Potts, and Fortuin--Kasteleyn in statistical physics. Prior to this work, deletion--contraction was also the fastest known general-purpose algorithm for these invariants, running in time roughly proportional to the number of spanning trees in the input graph. <rb> Here, we give a substantially faster algorithm that computes the Tutte polynomial---and hence, all the aforementioned invariants and more---of an arbitrary graph in time and space 2^nn^{O(1)}.
Joint work with Andreas Björklund, Thore Husfeldt, and Mikko Koivisto.

Speaker: Dr Petteri Kaski (HIIT)

Slides Talk-Kaski.pdf

10:20 Uniform sampling of local minima in Ising lattices

We present a combinatorial method for the uniform sampling of local energy minima in square and hexagonal 2D Ising spin glass lattices. The method has been used to estimate the number and energy distribution of local minima in lattices of up to 2000 spins.

Speaker: Prof. Pekka Orponen (TKK)

Slides orponen.pdf

10:40 break

11:00 Solution Counting for Combinatorial Problems: Exploiting BP, DPLL, and Statistics

We consider the problem of estimating the model count (number of solutions) of Boolean formulas, and present two techniques that compute estimates of these counts, as well as either lower or upper bounds with different trade-offs between efficiency, bound quality, and correctness guarantee. For lower bounds, we use a recent framework for probabilistic correctness guarantees, and exploit message passing techniques for marginal probability estimation, namely, variations of Belief Propagation (BP). Our results suggest that BP provides useful information even on structured loopy formulas. For upper bounds, we perform multiple runs of the MiniSat SAT solver with a minor modification, and obtain statistical bounds on the model count based on the observation that the distribution of a certain quantity of interest is often very close to the normal distribution. Our experiments demonstrate that our model counters, BPCount and MiniCount, based on these two ideas can provide very good bounds in time significantly less than alternative approaches.

Joint work with Lukas Kroc and Bart Selman.

Speaker: Dr Ashish Sabharwal (Cornell)

Slides Sabharwal-Nordita08.ppt

11:40 Lunch

13:00 Clusters and solution landscapes for vertex-cover and SAT problems

Speaker: Prof. Alexander Hartmann (University of Oldenburg)

Slides hartmann.pdf

13:40 break

14:00 Locked Constraint Satisfaction Problems

We introduce the random `locked' constraint satisfaction problems. When increasing the density of constraints, they display a broad `clustered' phase in which the space of solutions is divided into many isolated points. While the phase diagram can be found easily, these problems, in their clustered phase, are extremely challenging from the algorithmic point of view: the best known algorithms all fail to find solutions. We thus propose new benchmarks of really hard optimization problems and provide insight into the origin of their typical hardness.

Speaker: Lenka Zdeborova (U Paris-Sud)

Slides Lenka.pdf

14:20 Ark-less strategy for flood victims

In this talk, we will discuss (some) of the consequences of the phase transitions that arise in random constraint satisfaction problems, and present a simple strategy that allows to understand why it is so easy to find solutions in the clustered phase.

Speaker: Prof. Florent Krzakala (ESPCI, Paris)

Slides krzakala.pdf

14:40 Coffee

15:00 Learning to be lucky

Speaker: Prof. Matteo Marsili (Abdus Salam ICTP)

15:40 break

16:00 Contact patterns of inpatients in a regional healthcare system

In spite of advances in hospital treatment, hospitals continue to be a breeding ground for several airborne diseases and for diseases that are transmitted through close contacts like SARS, methicillin-resistant Staphylococcus aureus (MRSA), norovirus infections and tuberculosis (TB). Here we extract contact networks for up to 295,108 inpatients for durations up to two years from a database used for administrating a local public healthcare system serving a population of 1.9 million individuals. Structural and dynamical properties of the network of importance for the transmission of contagious diseases are then analyzed by methods from network epidemiology. The contact networks are found to be very much determined by an extreme (age independent) variation in duration of hospital stays and the hospital structure. We find that that the structure of contacts between in-patients exhibit structural properties, such as a high level of transitivity, assortativity and variation in number of contacts, that are likely to be of importance for the transmission of less contagious diseases. If these properties are considered when designing prevention programs the risk for and the effect of epidemic outbreaks may be decreased.

Speaker: Dr Petter Holme (Coputational Biology)

Slides petter_holme.pdf

16:20 The (many) phase transitions in random constraint satisfaction problems

Speaker: Prof. Federico Ricci-Tersenghi (Roma)

Slides RicciTersenghi.pdf

16:40 The Jarzynski identity: lessons from the Random Energy model

Speaker: Prof. Matteo Palassini (Barcelona)