Project submitted for the base funding of Artem Alikhanyan National Laboratory (ANL) I. Principal Investigator: Dr. Davit Sahakyan TITLE: Statistical physics of disordered systems and its interdisciplinary applications. Division, group: Theoretical department DURATION: 36 months Estimated Project Costs Estimated total cost of the project (US 45500 $) Including: Payments to Individual Participants 36000 Equipment Materials Other Direct Costs-books 500 Travel 9000 PROBLEM: Our main idea is to elaborate advanced methods of statistical physics of disordered systems, and apply them to the practically important tasks in diverse areas: evolution theory, economics, data mining, energy storage and conversion. The reason of such wide applications of statistical physics is that it developed flexible methods for dealing with many-body problems (physical degrees of freedom carrying energy and information, genes, strategically interacting agents in economics, streams of data). Within the evolution theory we will focus on investigating problems of virus evolution: extinction threshold, robustness, the finite population problem, recombination mechanisms. In solving these problems we shall apply non-perturbative methods of the spin-glass theory, the Hamilton-Jacobi equation formalism, and quantum field theory. Our solutions will apply to a variety of important practical problems, e.g., predicting virus diseases, the behavior of HIV virus, etc. Within the econophysics we shall solve models that have been applied by economists to the analysis of financial markets (multi-fractal random walk model and Markov switching model). Our hypothesis is that the crashes in financial markets are connected with specific phase transitions in these models, and, in principle, could be predicted. Within the data mining and inference theory we shall develop new, statistical physics-motivated algorithms for noisy data filtering and for parameter learning in the context of Hidden Markov Models, one of the main modeling tools in bioinformatics, statistics and information theory. We shall also apply the methods of statistical physics for analyzing the performance of the existing algorithms for filtration and parameter learning (e.g., Viterbi and Baum-Welch algorithms). Our basic method will be the theory of calculating Lyapunov indices (cycle expansion, zeta-functions) and methods developed for random-field lattice systems. Within the theory of cooling and energy storage we shall study thermodynamic limits of cooling: how much one can cool a physical substance given limited energy resources? The primary target of this research is in designing new approaches for dynamic nuclear polarization in NMR (nuclear magnetic resonance) physics. This subject of NMR-physics currently undergoes a renaissance due to implementing dynamic nuclear polarization in liquid-state NMR. Dynamic nuclear polarization presents a number of physical challenges, which are related to increasing the polarization storage time ( T1 relaxation time) and designing new physical methods for increasing the rate of polarization transfer. These issues belong to the realm of quantum statistical physics and will be studied within the current project. The subject promises new applications in MRI (magnetic resonance imaging) based medicine. Next, we shall determine whether and to which extent one can store useful energy (work) in equilibrium (primarily, microcanonical) states of a many-body physical system. The results will be applied for designing fast control systems operating via negative feedback. They will be also useful for developing new principles of energy accumulation and storage. II, III. OBJECTIVES and IMPACT: Virus evolution. We plan to develop an accurate theory for virus evolution that properly accounts for nonperturbative aspects of the phenomenon. This will improve predictions of future virus diseases, and will lead to a better understanding of the HIV virus and its evolution. In particular, we plan to develop the theory of HIV virus recombination. Many virologists claim that it is impossible to fight the HIV virus without understanding its recombination. We plan to give a mathematical theory for the reactions with few molecules, identify the statistical physics phases in the cell, and try to find some connection with these phases and the cancer phenomenon. We also plan to identify the statistical physics phases in the cell. Econophysics. We will solve (preferably exactly) several basic models for the economics of financial markets. Our exact solutions will improve the accuracy of predictions for future market crashes. In particular, we plan to find exact solution for the multi-fractal random model. Statistical physics of data mining and inference. As a result of our research we expect to find new algorithms for noisy data filtration and parameter learning. These algorithms will advance the fields of bioinformatics and automatic speech recognition, where it is necessary to have fast inference algorithms that (especially in bioinformatics) are integrated with the physical content of the problem. The proper theory for several widely applied data mining algorithms, e.g., the Viterbi algorithm for filtering and expectation-maximization (Baum-Welch) algorithm of parameter learning, is currently lacking. This prevents the understanding of their limitations and impedes their improvement. Our results will be relevant in this context. Cooling and energy storage. We shall develop new methods for dynamic nuclear polarization (spin cooling) based on the ideas of quantum control and quantum statistical mechanics. These methods can find applications in MRI (magnetic resonance imaging) that amounts to various methods for structural diagnostics of tissues 1 13 and organs. The main limitation of MRI is a small polarization of the H and/or C spins. This is precisely the problem addressed by dynamic nuclear polarization. We also expect that our results will lead to new design principles for energy storage and accumulation. Participating Institutions Task 1: Econophysics 1.1 Kiel University Solution of Multi-fractal Random walk model. Kiel University 1.2 Solution of the Markov switching models; determination of its phase structure. 1.3 Solution of continuous branching models and connection with conformal fieldtheoretical models. 1.4 Kiel University Application of our solutions to analyzing financial data. Comparison of different methods for predicting financial crashes. 1.5 Non-Hamiltonian statistical mechanics and its possible connection with econophysics. Research results will be delivered via publications in high-quality scientific journals on statistical physics and economics such as Phys. Rev. Lett., Physical Review E, JSTAT, The Journal of Financial and Quantitative Analysis, Quantitative Finance Financial and Quantitative Analysis Participating Institutions Task 2: Virus evolution models Academia Sinica 2.1 Limits of diffusion theory in population genetics. Fluctuation-dissipation relations in evolution. 2.2 Collective, non-perturbative phenomena in evolution theory. Evolution for finite populations. Rice University 2.3 Recombination phenomena in HIV. Microscopic finite population models of recombination and the role of lethal mutations. Interference of the mutation robustness and recombination. 2.4 Extinction threshold versus error threshold for virus populations. Research results will be delivered via publications in high-quality scientific journals on statistical physics and mathematical/theoretical biology such as Phys. Rev. Lett., Physical Review E, JSTAT, J. of Theoretical Biology, Mathematical Biosciences, PNAS, PLoS Biology Task 3: Design properties of the living matter, few-body chemical reactions and the cell modeling 3.1 Participating Institutions Seattle University Genotype-phenotype mapping and resonance phenomena. 3.2 Seattle University Stability of ecological communities: new ideas. 3.3 Vienna University Minimal models of autocatalytic reactions necessary for the life emergence. Statistical physics phases for the networks of chemical reactions. 3.4 Ecole Polytechnique Describing chemical reactions with few molecules. Research results will be delivered via publications in high-quality scientific journals on statistical physics and chemical physics such as Phys. Rev. Lett., Physical Review E, JSTAT, J. of Chem. Phys., J. of Physical Chemistry, Biophysical Journal Task 4: Inference and learning problems. 4.1 Theoretical analysis of the Viterbi filtering for discrete-space Hidden Markov Models (HMM) Participating Institutions University of Southern California (USC) via lstatistical mechanics. Random-field Ising and Potts models. Applicability of the functional renormalization group. 4.2 Soliton filtering of continuous-space HMM. Solitons in disordered potential. Non-linear filtering algorithms. Advantages and shortcomings of realizing filters via non-linear elements. Generalization of the Kalman’s filter. 4.3 Statistical mechanics of parameter learning for discrete-space HMM. The role of free energy, University of Southern California (USC) temperature and internal energy. 4.4 Statistical mechanics of the Occam’s razor. Research results will be delivered via publications in journals on statistical physics, artificial intelligence and machine learning such as Phys. Rev. Lett., Phys. Rev. E, JSTAT, J. of Machine Learning, IEEE-IT. Preliminary results will be reported in conference proceedings. Task 5: Cooling, polarization transfer and energy storage. 5.1 Thermodynamic limits of cooling: how much one can cool dynamically a quantum system Participating Institutions Stuttgart University with given energy levels and how much work has to be invested in this maximal cooling. Feasibility of realizing the optimal cooling schemes. 5.2 How much work can be extracted from a many-body system in a microcanonical equilibrium state via cyclically acting external fields. The meaning for the non-equivalence between the canonical and microcanonical ensembles in the context of work extraction. 5.3 Thermodynamics of quantum rotating systems. The thermodynamic meaning of the Coriolis force. 5.4 Theory of energy storage for biological systems. Energy storage in slowly relaxing Max-Planck Institute for Biological Cybernetics, degrees of freedom. Tuebingen 5.5 Trade-off between efficiency and complexity of molecular energy conversion processes. Research results will be delivered via publications in high-quality scientific journals on statistical physics and mathematical/theoretical biology such as Phys. Rev. Lett., Physical Review E, JSTAT, J. of Theoretical Biology. IV. The worldwide researches made on the project topic and the competitiveness of the project Virus evolution. Evolution research is necessary for understanding major problems of modern bio-medicine: emergence of new viruses, HIV and cancer. Within this proposal we shall solve several problems of the evolution research and apply them to concrete bio-medical problems. Interdisciplinary applications of statistical physics are important here [1--6], because evolution phenomena have very often essentially collective, non-perturbative character. They generate subtle structures with non-trivial mathematical description (“reasonable” approximations popular in mathematical biology, could overestimate the results in hundreds of times, see ). Hence for understanding general features of evolution we need microscopic models, where many-body effects can be analyzed non-perturbatively. To this end, it is necessary to employ statistical physics methods. Since 2004 our group actively publishes in this field [7--20]. Among our achievements is the exact solution of the Eigen’s model (an open problem since 1971). There are several strong groups applying statistical physics to evolution: D. Fisher, M. Deem, L. Peliti, K. Kaneko, E. Baake, M.Lassig, J. Krug, P. Schuster. We support scientific contacts with most of them. During the last 5-6 years our group derived more exact results in evolution theory than any other group. Methods from the spin-glass theory are especially useful here [21--23]. Also here our group has leading positions [24,25]. Econophysics. Recent years witnessed applications of statistical physics to the theory of financial markets (groups by E. Stanley, J.P. Bouchaud, D. Sornette, T.Lux) [26--28]. These groups employed ideas from scaling theory and spin-glass physics. Our group just started researching applications of statistical physics to financial markets. In collaboration with T. Lux (a world leader in econophysics) we recently related the models employed in data analysis of financial markets to spin glasses (Random Energy Model) and conformal field-theory. These observations will hopefully lead us to exact solutions for certain well known models of the finance theory (e.g., multi-fractal random walk) . Statistical physics of data mining and inference. Hidden Markov models (HMMs) is regarded to be one of the most successful statistical modeling tools that have emerged in the last 40-50 years [29--31]. They consist of two components: hidden states and observations. The hidden states are unobservable and form a Markov chain. The observations are independent conditionally on the states and provide the only available information about the state dynamics. Thus the observed stochastic process is generated by a Markov process observed via a memory-less noisy channel [29--31]. HMMs are widely employed in various areas of probabilistic modeling: information theory, signal processing, bioinformatics, mathematical economics, linguistics, etc. There are two reasons for this. First, HMM present simple and flexible models for a history-dependent random process. This is in contrast to the Markov process, where the history is irrelevant. Second, HMM provide the simplest situation, where structured data passes through a noisy channel. The inference problems of HMM naturally divide into two classes [29--31]: (i) recovering the hidden sequence of states given the observed sequence (filtering), and (ii) parameter learning, where the transition probabilities of the hidden Markov chain (and/or conditional probabilities of observations) are unknown and have to be determined from the observed sequence. There exist concrete methods for each class [29--31] (e.g., expectation-maximization algorithm, Baum-Viterbi method, etc). However, not much is known on the performance of these methods and on their possible limitations. Our premise – already partially supported via previous results by us and other groups -- is that reformulating these algorithms as statistical physics models will allow to gain information on their performance and will suggest new inference algorithms. Our previous experience in this subject includes developing an efficient method for calculating the entropy of HMM  (which is the first step towards analyzing theoretically inference algorithms), and statistical mechanics analysis of the Viterbi filtering algorithm . This work already uncovered certain basic limitations of the Viterbi algorithm. In the field of probabilistic learning we recently carried out a statistical physics analysis of the so called semi-supervised learning . Earlier, our group worked on related problems of developing statistical physics-based error-correcting for noisy channels [34--38]. Cooling. Nuclear Magnetic Resonance (NMR) is applied in many areas of modern science (physics, biology, chemistry, medicine) . Its application to medicine is best known as MRI (magnetic resonance imaging) and consists of various methods for structural diagnostics of tissues and organs (proton-NMR, carbon-13-NMR, chemical shift NMR) [40--42]. The main advantage of MRI compared to computed tomography and imaging methods based on radioactive tracers (nuclear medicine) is that MRI is able to record the dynamic state of tissues and organs; in particular, it is able to give real-time resolutions of various metabolic processes, flow effects (blood circulation) and tissue oxygenation [41,42]. Besides medical applications, this aspect is crucial for the bio-physical research . Till recently, most applications of MRI techniques are limited to the detection of water, because other substances are not sufficiently abundant and are not polarized sufficiently strongly. Both these factors lead to low sensitivity of MRI, which fundamentally originates from the low magnetic energy of nuclear spins compared with the thermal energy at room temperature [40-42]. Thus the main challenge for the efficient usage of MRI techniques is to increase dynamically (cooling) the spin polarization of basic NMR 13 15 1 substances (e.g., C , N , H ) which can be used, in particular, in endogenous medical substances . The same problem of cooling is of fundamental importance in applications of NMR to quantum information processors, NMR chemical spectroscopy, etc . The method of dynamic nuclear polarization (DNP) emerged recently as the main tool for cooling [40,42]. It consists of identifying highly polarized substances (usually these are electron spins with or without optical pumping; single electron 3 spin polarization is 10 times greater than that of the proton) and transferring this polarization to the target nuclear spin. The method was known in solid state NMR, but recently it is actively applied also in the liquid-state NMR that opens up new applications in medicine . Within this proposal we plan to develop new methods of cooling, and to analyze the principal limits for the existing methods. A. E. Allahverdyan works on cooling and NMR related areas since 2003. In 2003 he (together with Balian and Nieuwenhuizen) proposed a new method of spin tomography (state determination), which employed commutative quantum measurements only and was based on distributing the target spin state between several spin systems . In 2007 the new method was experimentally realized in the Dortmund NMR group on a liquid-state NMR system . In 2004 Allahverdyan et al. proposed a new method of dynamical spin cooling that does not use the conventional polarization resources (e.g., electronic spins), but instead finds polarization resources in a phononic thermal bath . In 2006 Allahverdyan and Petrosyan proposed a new mechanism of cooling in two-temperature NMR systems . This mechanism was based on a new scenario of phase transition for this non-equilibrium system. In 20092010 Allahverdyan (together with Hovhannisyan and Mahler) studied the principal limitations for cooling arising from quantum mechanics [48,49]. Energy storage and quantum thermodynamics. The basic purpose of thermodynamics is in studying energy transformation, storage and utilization by various machines [50--52]. Though in its historical development thermodynamics concentrated on macroscopic machines, it became nowadays obvious that many important machines are of micro and nanoscale . Living organisms are integrations of functionally diverse molecular machines, due to which we can walk, talk, and think. Equally important are the artificial machines constructed on small scales . A common prediction is that the progress in miniaturization of devices will open the way to new technologies in various fields. The necessity of understanding the processes of energy storage and transformation at the nanoscale, with a full account for quantum effects, motivated the development of the field of quantum thermodynamics; see [50,51] for reviews. This subject studies processes of work (useful energy) extraction with help of a finite (nanoscale) engine, energy storage in nanoscale batteries, energy exchange between interacting finite systems, microscopic theories of restitution coefficients, the energy transfer and storage in rotating systems (encountered in ATP, the basic battery of the biological energy), etc. Some of these problems will be studied within the present proposal. A.E. Allahverdyan is one of the founders of quantum thermodynamics. His work with Nieuwenhuizen in 2000 on non-trivial mechanisms of energy storage in the quantum situation initiated this field; see also [53--65]. V. Personnel Commitments (chart, total number of project participants, responsibilities of each). 1. Leading researcher Dr. D.B. Sahakyan, the PI of the project. 2. Senior researcher Dr. A. E. Allahverdyan. 3. Researcher Z. Kirakossyan, phd student. 4. Research assistant К. Hovhannisyan, phd student. The average age of participants is 35, there are 2 participants younger than 35, and nobody is retired. Work plan: Task 1: Sahakyan and Kirakossyan (1.1—1.4). Sahakyan and Allahverdyan (1.5). Task 2: Sahakyan and Kirakossyan. Task 3: Sahakyan, Allahverdyan and Hovhannisyan. Task 4: Allahverdyan (4.1—4.4). Sahakyan (4.4) Task 5: Allahverdyan and Hovhannisyan (5.1—5.5). Sahakyan (5.4). Equipment 200 $ 3 Cartrages for the printer Total Подробное описание заказываемого оборудования, указание сайта фирмы. Materials Paper, pens 150 $ Direct cost description Cost (US $) Other Direct Costs Travel costs (US $) CIS travel International travel 9000 Total 9000 VI Technical Approach and Methodology Task 1: Econophysics is a field, where the problems of economics are studied using methods of theoretical (in particular, statistical) physics. Statistical physics is applicable, because there are many degrees of freedom (agents, goods) and quantities that have certain features of energy (money, value). The main postulate of statistical physics is the ergodic/mixing hypothesis (maximum entropy principle). Its analogue in economics is the concept of self-regulating market. One of the main tools of statistical physics is the scaling relations, which were successfully applied to economics in . Mandelbrot and co-authors suggested to apply multi-fractal models for describing stock fluctuations in financial markets . This is more realistic than modeling them via Brownian motion. Further advances in this field relate to Markov-switching multi-fractal models (MSM), which recover the timetranslation symmetry lacking in the previous models. Nowadays MSM is a very popular tool for analyzing market data . According to our preliminary results, there is an exact mapping between multi-scaling models and the Random Energy Model [21--23] (one of the paradigmatic models of the spin-glass theory). This mapping can be used for improving the accuracy of econometric calculations, identifying the market’s phase structure, and predicting financial crashes. Our idea is to identify those crashes by looking to the high frequency fluctuations of the market. In the statistical physics language this corresponds to the spin-glass phase transition. When mapping the concepts of economics to statistical thermodynamics, we realized that the main difference is that the first law of thermodynamics is lacking in economics. This is why we will try to use a weaker form of statistical mechanics (non-Hamiltonian statistical mechanics) for modeling economics. Task 2.1: The diffusion equation is certainly the main working mathematical method of population genetics [94,95]. Within this task we shall understand whether this method applies to the strong selection situation, which is typical for viruses and bacteria. According to our preliminary results it does not apply and should be replaced by the Hamilton-Jacobi approach . Task 2.2: The finite population problem is one of the central topics in the evolution research. Recently there have been several serious attempts of solving this problem. They however contradict each other [96,97]. Ref.  widely used the solitary wave concept, which is borrowed from the infinite population evolution research. As we have carefully checked in our article , the concept of solitary wave is completely wrong for infinite populations. We plan to perform some numeric and theoretical analysis to clarify the applicability of this concept to finite populations. Task 2.3: Here we should understand the role of robustness in evolution systems and its relation to recombination. There were many theoretical speculations about possibility of a selection via flatness instead of selection via fitness. However, such a situation was experimentally observed only recently . Interestingly, the robustness can increase the role of recombination ; see also the recent review about recombination phenomenon . We will study the interference of recombination and robustness via an analytical theory. This will lead to understanding dynamic aspects of robustness. Within this task we shall also develop a simplified theory of recombination. To this end we will consider a quasi-linkage equilibrium situation, suggested by Kimura, and apply to it fluctuation-dissipation relations. We observe that different quantities in evolution have either mean-field or fluctuating behavior. We will use this observation to simplify complicated mathematical machinery of recombination theory by ideas and methods of statistical mechanics. Task 2.4: There are two views among the virologists about extinction of virus populations at high mutation rate. It could be explained using either the concept of error threshold, or the extinction threshold [92,93]. We shall understand how to define the correct extinction threshold in the case of lethality. This issue is important for both virology and the origin of life research. Task 3.1: Understanding of the genotype-phenotype mapping is an important subject of bio-medical research [75,76]. There is much room here for new ideas and approached from statistical physics, e.g., Ref.  suggested that the phenotype properties were shaped together with mutational robustness during the evolution. We shall study the genotype-phenotype mapping from the information theoretical viewpoint, employing our previous experience in relating statistical physics to information theory [35--39]. We shall attempt to define a design temperature for genotype-phenotype mapping, and try to understand the role of RNA in this mapping. Task 3.2: This problem arose when ecological modelers noted that substantially random interaction between various species will never support the population stability observed in nature [77,78]. Hence one should look for some design of inter-species interaction, which came out during evolution. We shall study a modified version of the multi-species interaction model  from the information -theoretical viewpoint. In particular, we shall attempt to describe how information is transferred from the couplings of multispecies interaction to the frequencies of different species. Task 3.3: Ref.  proposed to decribe the living matter as a set of auto-catalyzing reactions. This idea was elaborated in . Later on Ref.  suggested modeling the cell trough a limit cycle of the proteinprotein interaction network; see  for a review. There is a substantial room for new ideas here, e.g., because the microscopic mechanism of the cell differentiation  is not captured by the existing models . Our plan is to analyze the minimal version of autocatalytic reactions necessary for the life modeling. We will also analyze all possible phases for the autocatalytic reactions [84--86] and select the most relevant one for the emergence of life. We expect that different aspects of the cell dynamics -metabolism, information processing, control and the interaction with other cells -- are reflected in the internal hidden state of the cell. We also expect that our ideas will be useful for understanding the purposeful behavior, the main characteristic feature of the living matter. Task 3.4: The number of molecules participating in the cell dynamics is sometimes rather small. This makes inapplicable the standard methods of chemical physics. We shall apply to this situation the Hamilton-Jacobi approach , which was recently developed in our work . We are interested mainly by chemical master equation with two connected chains of equations . Task 4.1: We shall employ methods from the theory of disordered lattice models (statistical mechanics). This includes functional renormalization group , embedded Markov technique , etc. Task 4.2: The specific point of this problem is that one ought to study solitons moving i n a disordered potential . Hence we shall most probably have to work out a generalization of standard soliton theory methods  (e.g., inverse scattering method) to this situation. Task 4.3: We intend to investigate this problem via the zeta-function method  for Hidden Markov Models . Task 4.4: The problem will be approached via the disorder-dominated renormalization group  and the Bayesian field theory [72,73]. Tasks 5.1 – 5.2: For understanding this problem we need to solve a (typically high-dimensional) optimization problem in the joint space of physical states (density transformations) and dynamic transformations (unitary operators). Work is currently in progress to develop effective optimization methods for this solving such problems. Task 5.3: We need to understand foundations of statistical mechanics as seen from a non-intertial frame. Task 5.4: A detailed understanding of the meta-stability theory for Markov chains is needed . We also expect to use the majorization theory results. Task 5.5: We shall approach this problem from the stands of modern computational complexity . References. 1. M. Eigen, Naturwissenschaften 58, 465 (1971). 2. M. Eigen, J. Mc Caskill, and P. Schuster, Molecular quasi-species, Adv. Chem. Phys. 75, 149 (1989) 3. E. Baake, M. Baake, H. Wagner, Phys. Rev. Let. 78, 559 (1997). 4. E. Baake, W. Gabriel, Ann. Review Comp. Phys. 7,203 (2000). 5. B. Drossel, Advances in Physics 50, 209 (2001). 6. D.B. Saakian, C.K. Hu, Eigen model as a quantum spin chain: exact dynamics, Phys. Rev. E, 69, 021913 (2004). 7. D.B.Saakian and C.K. Hu, Solvable biological evolution model with a parallel mutation-selection scheme, Phys. Rev. E, 69, 046121 (2004). 8. D.B. Saakian, C.K. Hu and H. Khachatryan, Solvable biological evolution models with general fitness functions and multiple mutations in parallel mutation-selection scheme, Phys. Rev. E, 70, 041908 (2004). 9. D.B.Saakian, Error threshold in optimal coding, numerical criteria and classes of universalities for complexity.Phys. Rev. E, 71, 016126 (2005). 10. D. B. Saakian, E. Munoz, C.-K. Hu, and M. W. Deem, Quasispecies theory for multiple-peak fitness landscapes, Phys. Rev. E 73, 041913 (2006). 11. D. B. Saakian and C.-K. Hu, Exact solution of the Eigen model with general fitness functions and degradation rates, PNAS (USA) 103, 4935 (2006). 12. D.B. Saakian, A new method for the solution of models of biological evolution: Derivation of exact steady-state distributions, J. Stat. Physics, 128, 781 (2007). 13. D.B. Saakian, Z. Kirakossyan, C.K. Hu, Diploid Biological Evolution Models with General Smooth Fitness Landscapes, Phys. Rev. E, 77, 061907 (2008). D.B. Saakian, O. Rozanova, A. Akmetzhanov, Exactly solvable dynamics of the Eigen and the Crow-Kimura model, Phys. Rev. E 78, 041908 (2008). 14. D. B. Saakian, Evolution models with base substitutions, insertions, deletions and selection, Phys. Rev. E, 78, 061920 (2008). 15. D. B. Saakian, C. K. Biebricher, C.-K. Hu, Phase diagram for the Eigen quasispecies theory with the truncated fitness landscape, Phys.Rev.E, 79. 041905 (2009). 16. D. B. Saakian and J. F. Fontanari, Evolutionary dynamics on rugged fitness landscapes: Exact dynamics and information theoretical aspects, Phys. Rev. E 80 041903 (2009). 17. Zh. Avetisyan, D.B. Saakian, Recombination in one and two dimensional fitness landscapes, Phys.Rev.E. 81, 051916 (2010). 18. D. B. Saakian , A. S. Martirosyan and C. K. Hu, Phys. Rev. E 81, 061913 (2010). Different fitnesses for in vivo and in vitro evolutions due to the finite generation-time effect. 19. Z. Kirakosyan, D.B. Saakian, and C.-K. Hu, Phys. Rev. E 82, 011904 (2010). Evolution models with lethal mutations on symmetric or random fitness landscapes. 20. D.B. Saakian and C.-K. Hu, Phys. Rev. E 82, 011902 (2010). Selection via flatness as a dynamical effect in evolution models with finite population. 21. B. Derrida, Phys. Rev. B. 24, 2613 (1981). 22. Y. V. Fyodorov and J. P. Bouchaud, J. Phys. A 41, 372001 (2008). 23. Y.V. Fyodorov, P. Le Doussal and A. Rosso, JSTAT P10005 (2009) 24. D.B. Saakian, Phase structure of string theory and the Random Energy Model, JSTAT, P07003 (2009). 25. D.B. Saakian, String correlation functions on a hierarchic tree, JSTAT, P03031 (2010). 26. P. Jackel, Monte-Carlo Methods in Finance (J. Wiley and Sons, Sussex, 2002) 27. R. Mantegna and H. E. Stanley, Econophysics (Cambridge University Press, Cambridge, 2004). 28. B. Mandelbrot, Fractals and scaling in finance (Springer, New-York, 1997). 29. L. R. Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition, Proc. IEEE, 77, 257 (1989). 30. Y. Ephraim and N. Merhav, Hidden Markov processes, IEEE Trans. Inf. Th., 48, 1518-1569, (2002). 31. P. Baldi and S. Brunak, Bioinformatics: The Machine Learning Approach (MIT Press, Cambridge, USA, 2001). 32. A. E. Allahverdyan, Entropy of Hidden Markov Processes via Cycle Expansion, J. Stat. Phys. 133, 535 (2008). 33. A.E. Allahverdyan and A. Galstyan, On Maximum a Posteriori Estimation of Hidden Markov Processes, in proceedings of Uncertainty in Artificial Intelligence, 2009. 34. A. E. Allahverdyan, G. Ver Steeg and A. Galstyan, Community detection with and without prior information, EPL, 90, 18002 (2010). 35. D. B. Saakian, JETP Lett. 61, 610 (1995). 36. D.B. Saakian, Error threshold in optimal coding, numerical criteria and classes of universalities for complexity, Phys. Rev. E, 71 016126 (2005). 37. D. B. Saakian, Teor. Mat. Fiz. 97, 1199 (1993). 38. A. E. Allakhverdyan and D. B. Saakian, JETP 111, 1410 (1997). 39. A. E. Allahverdyan and D. B. Saakian, Nucl. Phys. B 498, 604 (1997). 40. R.L Haner and P.A. Keifer, Encyclopedia of Magnetic Resonance (John Wiley, NY, 2009) 41. A. M. Blamire, The British Journal of Radiology, 81, 601 (2008). The technology of MRI — the next 10 years? 42. J. H. Ardenkjaer-Larsen et al., PNAS, 100, 10158 (2003). Increase in signal-to-noise ratio of >10,000 times in liquid-state NMR 43. A. E. Allahverdyan, Roger Balian and Th.M. Nieuwenhuizen, Phys. Rev. Lett. 92, 120402 (2004). Determining a quantum state by means of a single apparatus 44. X. Peng, J. Du and D. Suter, Phys. Rev. A 76, 042117 (2004). Measuring complete quantum states with a single observable. 45. A. E. Allahverdyan, R. Serral Gracia and Th.M. Nieuwenhuizen, Phys. Rev. Lett., 93, 260404 (2004). Bath-assisted cooling of spins. 46. A. E. Allahverdyan and K. G. Petrosyan, Phys. Rev. Lett. 96, 065701 (2006). Anomalous Latent Heat in Nonequilibrium Phase Transitions 47. A. E. Allahverdyan and K. Hovhannisyan, Phys. Rev. A 81, 012312 (2010). Transferring elements of density matrix 48. A. E. Allahverdyan, K. Hovhannisyan and G. Mahler, Phys. Rev. E 81, 051129 (2010). Optimal refrigerator 49. K. Hovhannisyan and A. E. Allahverdyan, J. Stat. Mech. (2010) P06010. Thermodynamics of enhanced heat transfer: a model study 50. A. E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen, Journal of Modern Optics, 51, 2703 (2004). Quantum thermodynamics: thermodynamics at the nanoscale. 51. J. Gemmer, M. Michel and G. Mahler, Quantum Thermodynamics (Springer, NY, 2004). 52. V. Balzani, A. Credi and M. Venturi, Molecular Devices and Machines - A Journey into the Nano World (Wiley-VCH, Weinheim, 2003). 53. A.E. Allahverdyan and Th.M. Nieuwenhuizen, Phys. Rev. Lett., 85, 1799, (2000). Extraction of work from a single thermal bath in the quantum regime. 54. A.E. Allahverdyan and Th.M. Nieuwenhuizen, Phys. Rev. Lett., 85, 232, (2000). Optimizing the classic heat engine. 55. A.E. Allahverdyan, R. Balian and Th.M. Nieuwenhuizen, Europhysics Letters, 67, 565, (2004). Maximal work extraction from quantum systems. 56. A. E. Allahverdyan, D. Janzing and G. Mahler, JSTAT, P09011 (2009). Thermodynamic efficiency of information and heat flow. 57. A. E. Allahverdyan, R. S. Johal and G. Mahler, Phys. Rev. E, 77, 041118 (2008). Work extremum principle: Structure and function of quantum heat engines. 58. A. E. Allahverdyan and Th. M. Nieuwenhuizen, Phys. Rev. E, 75, 051124 (2007). Minimal-work principle and its limits for classical systems 59. A. E. Allahverdyan and Th. M. Nieuwenhuizen, Phys. Rev. E, 73, 066119 (2006). Explanation of the Gibbs paradox within the framework of quantum thermodynamics 60. A. E. Allahverdyan and Th. M. Nieuwenhuizen, Phys. Rev. E 71, 046107 (2005). Minimal work principle: Proof and counterexamples 61. A. E. Allahverdyan, R. Serral Gracià, and Th. M. Nieuwenhuizen, Phys. Rev. E 71, 046106 (2005). Work extraction in the spin-boson model 62. A.E. Allahverdyan, R. Balian and Th. M. Nieuwenhuizen, Entropy, 6, 30 (2004). Thomson's formulation of the second law for macroscopic and finite work sources. 63. A.E. Allahverdyan and Th.M. Nieuwenhuizen, Physica A, 305, 542 (2002). A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium. 64. A.E. Allahverdyann and Th.M. Nieuwenhuizen, Phys. Rev. E, 66, 036102, (2002). Statistical thermodynamics of quantum brownian motion. 65. A.E. Allahverdyan, Th.M. Nieuwenhuizen, Phys. Rev. E, 62, 845, (2000). Steady adiabatic state : Its thermodynamics, entropy production, energy dissipation and violation of Onsager relations. 66. D. Ruelle, Statistical Mechanics, Thermodynamic Formalism, (Reading, MA: Addison-Wesley, 1978). 67. R. K. Dodd et al., Solitons and non-linear wave-equations (Academic Press, London, 1984). 68. V.M. Loginov, Soliton of the Korteweg-de Vries equation: a device for separating an additive mixture of signal and Gaussian noise, JETP, 105, 796 (1994). 69. F. Igloi and C. Monthus, Strong disorder RG approach of random systems, arXiv:cond-mat/0502448. 70. A. N. Chetaev, Neural Networks and Markov Chains (Moscow, Nauka, 1985). 71. G. Ausiello, et al., Complexity and Approximation: Combinatorial optimization problems and their approximability properties (Springer-Verlag, Berlin, 1999). 72. J. C. Lemm, Bayesian Field Theory: Nonparametric Approaches to Density Estimation, Regression, Classification, and Inverse Quantum Problems, arXiv:physics/9912005. 73. J. C. Lemm, J. Uhlig, A. Weiguny, A Bayesian Approach to Inverse Quantum Statistics, Phys. Rev. Lett. 84, 2068 (2000). 74. L. Calvet and A. Fisher, How to forecast long-run volatility: Regime switching and the estimation of multifractal processes, J. Fin. Econometrics, 2, 49 (2004). 75. A. Sakata, K. Hukushima, K. Kaneko, Funnel Landscape and Mutational Robustness as a Result of Evolution under Thermal Noise, Phys. Rev. Lett. 102, 148101 (2009). 76. S. Ciliberti, O. C. Martin, A. Wagner, Innovation and robustness in complex regulatory gene networks, PNAS, 104, 13591 (2007). 77. R. M. May, Nature 238, 413 (1972). 78. E. Thibault et al. Stability of Ecological Communities and the Architecture of Mutualistic and Trophic Networks, Science 329, 853 (2010). 79. M. Eigen and P. Schuster. The Hypercycle - A Principle of Natural Self-Organization, Naturwissenschaften, 64, 541 (1977); 65, 7 (1978); 65, 341 (1978). 80. S. Kaufmann, The origins of order: self-organization and selection in evolution. (Oxford University Press, Oxford, UK, 1993). 81. L. Kadanoff, Physics Today, 8 (2009). 82. K. Kaneko, Life: An Introduction to Complex Systems Biology (Springer, NY, 2006). 83. F.F. Costa, Non-coding RNAs, epigenetics and complexity, Gene, 410, 9 (2008). 84. Y. Togashi and K. Kaneko, Transitions Induced by the Discreteness of Molecules in a Small Autocatalytic System, Phys. Rev. Lett. 86, 2459 (2005). 85. A. Awazu and K. Kaneko, Ubiquitous glassy relaxation in catalytic reaction networks, Phys. Rev. E 80, 041931 (2009). 86. A. Awazu and K. Kaneko, Discreteness-induced slow relaxation in reversible catalytic reaction networks, Phys. Rev. E 81, 051920 (2010). 87. M. I. Dykman, E. Mori, J. Ross, and P. M. Hunt, J. Chem. Phys. 100, 5735 (1994). 88. D. A. Beard, H. Qian, Chemical Biophysics: Quantitative Analysis of Cellular Systems (Cambridge Texts in Biomedical Engineering, Cambridge Univ. Press, NY, 2008). 89. R. Sanjuan, J. M. Cuevas, V. Furio, E. C. Holmes, A. Moya, Selection for Robustness in Mutagenized RNA Viruses, PLoS Gen. 3, 93 (2007). 90. G. J. Szollsosi and I. Derenyi, The Effect of Recombination on the Neutral Evolution of Genetic Robustness, Mathematical Biosciences 214, 58 (2008). 91. J. Arjan, G. M. de Visser and S. F. Elena, Resolving the paradox of sex and recombination, Nature Review genetics, 8,139 (2007). 92. J.J. Bull and C.O. Wilke, Lethal mutagenesis of bacteria. Genetics 180,1061 (2008). 93. H. Tejero, A. Marín, F. Montero, Effect of lethality on the extinction and on the error threshold of quasispecies, J. of Theor. Biol., 262, 733 (2010). 94. W. J. Ewens, Mathematical Population Genetics (Springer-Verlag, Berlin, 2004). 95. R. Burger, The mathematical theory of selection, recombination, and mutation (Wiley, NY, 2000). 96. M.M. Desai, D.S. Fisher, A.W. Murray, The speed of evolution and maintenance of variation in asexual populations, Curr. Biol. 17, 385 (2007). 97. I.M. Rouzine, E. Brunet, C.O. Wilke, The traveling-wave approach to asexual evolution: Muller’s ratchet and speed of adaptation. Theor. Popul. Biol. 73, 24 (2008).