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1.	Rydving, Erik, et al. (författare) Do Gedanken experiments compel quantization of gravity? 2021 Ingår i: Physical Review D. - : American Physical Society (APS). - 2470-0010 .- 2470-0029. ; 104:8 Tidskriftsartikel (refereegranskat)abstract Whether gravity is quantized remains an open question. To shed light on this problem, various Gedanken experiments have been proposed. One popular example is an interference experiment with a massive system that interacts gravitationally with another distant system, where an apparent paradox arises: even for spacelike separation the outcome of the interference experiment depends on actions on the distant system, leading to a violation of either complementarity or no-signaling. A recent resolution shows that the paradox is avoided when quantizing gravitational radiation and including quantum fluctuations of the gravitational field. Here we show that the paradox in question can also be resolved without considering gravitational radiation, relying only on the Planck length as a limit on spatial resolution. Therefore, in contrast to conclusions previously drawn, we find that the necessity for a quantum field theory of gravity does not follow from so far considered Gedanken experiments of this type. In addition, we point out that in the common realization of the setup the effects are governed by the mass octopole rather than the quadrupole. Our results highlight that no Gedanken experiment to date compels a quantum field theory of gravity, in contrast to the electromagnetic case.
2.	Alava, Mikko, et al. (författare) Circumspect descent prevails in solving random constraint satisfaction problems 2008 Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : Proceedings of the National Academy of Sciences. - 0027-8424 .- 1091-6490. ; 105:40, s. 15253-15257 Tidskriftsartikel (refereegranskat)abstract We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large K-SAT instances almost surely in linear time, up to high clause-to-variable ratios a; for example, for K = 4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.
3.	Ameur, Adam, et al. (författare) Global gene expression analysis by combinatorial optimization 2004 Ingår i: In Silico Biology. - 1386-6338. ; 4 Tidskriftsartikel (refereegranskat)abstract Generally, there is a trade-off between methods of gene expression analysis that are precise but labor-intensive, e.g. RT-PCR, and methods that scale up to global coverage but are not quite as quantitative, e.g. microarrays. In the present paper, we show how how a known method of gene expression profiling (K. Kato, Nucleic Acids Res. 23, 3685-3690 (1995)), which relies on a fairly small number of steps, can be turned into a global gene expression measurement by advanced data post-processing, with potentially little loss of accuracy. Post-processing here entails solving an ancillary combinatorial optimization problem. Validation is performed on in silico experiments generated from the FANTOM data base of full-length mouse cDNA. We present two variants of the method. One uses state-of-the-art commercial software for solving problems of this kind, the other a code developed by us specifically for this purpose, released in the public domain under GPL license.
4.	Ardelius, John, et al. (författare) Behavior of heuristics on large and hard satisfiability problems 2006 Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 74:3, s. 037702- Tidskriftsartikel (refereegranskat)abstract We study the behavior of a heuristic for solving random satisfiability problems by stochastic local search near the satisfiability threshold. The heuristic for average satisfiability (ASAT), is similar to the Focused Metropolis Search heuristic, and shares the property of being focused, i.e., only variables in unsatisfied clauses are updated in each step. It is significantly simpler than the benchmark WALKSAT heuristic. We show that ASAT solves instances as large as N=10(6) in linear time, on average, up to a ratio of 4.21 clauses per variable in random three-satisfiability. For K higher than 3, ASAT appears to solve instances of K-satisfiability up to the Montanari-Ricci-Tersenghi-Parisi full replica symmetry breaking (FSRB) threshold denoted alpha(s)(K) in linear time.
5.	Ardelius, John, et al. (författare) Clustering of solutions in hard satisfiability problems 2007 Ingår i: Journal of Statistical Mechanics: Theory and Experiment. - 1742-5468. ; :10, s. P10012- Tidskriftsartikel (refereegranskat)abstract We study numerically the solution space structure of random 3-SAT problems close to the SAT/UNSAT transition. This is done by considering chains of satisfiability problems, where clauses are added sequentially to a problem instance. Using the overlap measure of similarity between different solutions found on the same problem instance, we examine geometrical changes as a function of α. In each chain, the overlap distribution is first smooth, but then develops a tiered structure, indicating that the solutions are found in well separated clusters. On chains of not too large instances, all remaining solutions are eventually observed to be found in only one small cluster before vanishing. This condensation transition point is estimated by finite size scaling to be αc = 4.26 with an apparent critical exponent of about 1.7. The average overlap value is also observed to increase with α up to the transition, indicating a reduction in solutions space size, in accordance with theoretical predictions. The solutions are generated by a local heuristic, ASAT, and compared to those found by the Survey Propagation algorithm up to αc.
6.	Ardelius, John, 1978- (författare) On state space structure and average case complexity in random K-SAT problems 2008 Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract This thesis gives an introduction to a currently active area in the cross-section between theoretical computer science and theoretical physics. In the last ten years it has been suggested that critical behaviour, usually seen in models from condensed matter physics, may be responsible for the intractability of NP complete computation problems. This would suggest a very deep connection between the two fields on the most fundamental level. How deep this connection really is is subject to ongoing research as well as the topic of this thesis. Some of the conjectrues from the physics community regarding computational hardness in certain problem classes has turned out to be wrong or misinterpreted but the gained interest in both fields has promising potiential in moving the research frontier forward. The material presented in this thesis is the result of nearly two years work in trying to clearify how the results from physics can be interpreted in the language of actuall computation problems.
7.	Aurell, Erik, et al. (författare) A Cavity Master Equation for the continuous time dynamics of discrete spins models Annan publikation (övrigt vetenskapligt/konstnärligt)abstract We present a new method to close the Master Equation representing the continuous time dynamics of Ising interacting spins. The method makes use of the the theory of Random Point Processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean field ferromagnet and the dynamics of the one dimensional Ising system. We then present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the Random Field Ising model, and the Viana-Bray spin-glass model.
8.	Aurell, Erik, et al. (författare) A closure for the master equation starting from the dynamic cavity method 2023 Ingår i: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 56:17 Tidskriftsartikel (refereegranskat)abstract We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner using the theory of Random Point Processes. Within this approach, the master equation governing the system's dynamics is closed via a set of differential equations for the auxiliary cavity probabilities. The numerical results improve on the earlier versions of the closure on several important classes of problems. We re-visit here the cases of the Ising ferromagnet and the Viana-Bray spin-glass model.
9.	Aurell, Erik, et al. (författare) A message-passing scheme for non-equilibrium stationary states 2011 Ingår i: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT. - 1742-5468. ; , s. P04014- Tidskriftsartikel (refereegranskat)abstract We study stationary states in a diluted asymmetric (kinetic) Ising model. We apply the recently introduced dynamic cavity method to compute magnetizations of these stationary states. Depending on the update rule, different versions of the dynamic cavity method apply. We here study synchronous updates and random sequential updates, and compare local properties computed by the dynamic cavity method to numerical simulations. Using both types of updates, the dynamic cavity method is highly accurate at high enough temperatures. At low enough temperatures, for sequential updates the dynamic cavity method tends to a fixed point, but this does not agree with numerical simulations, while for parallel updates, the dynamic cavity method may display oscillatory behavior. When it converges and is accurate, the dynamic cavity method offers a huge speed-up compared to Monte Carlo, particularly for large systems.
10.	Aurell, Erik, et al. (författare) A physics-style approach to scalability of distributed systems 2005 Ingår i: Lecture Notes in Computer Science. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 0302-9743 .- 1611-3349. ; 3267, s. 266-272 Tidskriftsartikel (refereegranskat)abstract Is it possible to treat large scale distributed systems as physical systems? The importance of that question stems from the fact that the behavior of many P2P systems is very complex to analyze analytically, and simulation of scales of interest can be prohibitive. In Physics, however, one is accustomed to reasoning about large systems. The limit of very large systems may actually simplify the analysis. As a first example, we here analyze the effect of the density of populated nodes in an identifier space in a P2P system. We show that while the average path length is approximately given by a function of the number of populated nodes, there is a systematic effect which depends on the density. In other words, the dependence is both on the number of address nodes and the number of populated nodes, but only through their ratio. Interestingly, this effect is negative for finite densities, showing that an amount of randomness somewhat shortens average path length.
11.	Aurell, Erik, et al. (författare) A Physics-Style Approach to Scalability of Distributed Systems 2005. - 1 Ingår i: Global Computing. - Berlin, Heidelberg : Springer. - 9783540241010 ; , s. 266-272 Bokkapitel (refereegranskat)abstract Is it possible to treat large scale distributed systems as physical systems? The importance of that question stems from the fact that the behavior of many P2P systems is very complex to analyze analytically, and simulation of scales of interest can be prohibitive. In Physics, however, one is accustomed to reasoning about large systems. The limit of very large systems may actually simplify the analysis. As a first example, we here analyze the effect of the density of populated nodes in an identifier space in a P2P system. We show that while the average path length is approximately given by a function of the number of populated nodes, there is a systematic effect which depends on the density. In other words, the dependence is both on the number of address nodes and the number of populated nodes, but only through their ratio. Interestingly, this effect is negative for finite densities, showing that an amount of randomness somewhat shortens average path length. This work is funded by the Swedish funding agency VINNOVA, PPC project and the European PEPITO and EVERGROW projects.
12.	Aurell, Erik, et al. (författare) A physics-style approach to scalability of distributed systems 2004. - 1 Rapport (övrigt vetenskapligt/konstnärligt)abstract BEGIN example. Is it possible to treat large scale distributed systems as physical systems? The importance of that question stems from the fact that the behavior of many P2P systems is very complex to analyze analytically, and simulation of scales of interest can be prohibitive. In Physics, however, one is accustomed to reasoning about large systems. The limit of very large systems may actually simplify the analysis. As a first step, we here analyze the effect of the density of populated nodes in an identifier space in a P2P system. We show that while the average path length is approximately given by a function of the number of populated nodes, there is a systematic correction which depends on the density. In other words, the dependence is both on the number of address nodes and the number of populated nodes, but only through their ratio. Interestingly, the correction is negative for finite densities, showing that an amount of randomness somewhat shortens average path length. END of example.
13.	Aurell, Erik, et al. (författare) A trading agent built on constraint programming 2002. - 2 Konferensbidrag (refereegranskat)abstract The Trading Agent Competition (TAC) combines a fairly realistic model of the Internet commerce of the future, including shopbots and pricebots, with a challenging problem in automated reasoning and decision making. Automated trading via auctions under severe time constraints are to be con-ducted by entering autonomous agents into TAC, assuming the role of travel agents. The TAC game rules, as well as a description of the discrete op-timization problem faced by an agent that wishes to allocate goods to its clients, are described. The TAC’01 entry “006”, encapsulating a constraint programming solution, is explained in some detail.
14.	Aurell, Erik, et al. (författare) An inventory of Lattice Boltzmann models of multiphase flows 2001. - 1 Annan publikation (övrigt vetenskapligt/konstnärligt)abstract This document reports investigations of models of multiphase flows using Lattice Boltzmann methods. The emphasis is on deriving by Chapman- Enskog techniques the corresponding macroscopic equations. The singular interface (Young-Laplace-Gauss) model is described briefly, with a discussion of its limitations. The diffuse interface theory is discussed in more detail, and shown to lead to the singular interface model in the proper asymptotic limit. The Lattice Boltzmann method is presented in its simplest form appropriate for an ideal gas. Four different Lattice Boltzmann models for non-ideal multi-phase) isothermal flows are then presented in detail, and the resulting macroscopic equations derived. Partly in contradiction with the published literature, it is found that only one of the models gives physically fully acceptable equations. The form of the equation of state for a multiphase system the density interval above the coexistance line determines surface tension and interface thickness in the diffuse interface theory. The use of this relation for optimizing a numerical model is discussed. The extension of Lattice Boltzmann methods to the non-isothermal situation is discussed.
15.	Aurell, Erik, et al. (författare) An operator derivation of the Feynman-Vernon theory, with applications to the generating function of bath energy changes and to an-harmonic baths 2020 Ingår i: Journal of Physics A. - : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 53:27 Tidskriftsartikel (refereegranskat)abstract We present a derivation of the Feynman-Vernon approach to open quantum systems in the language of super-operators. We show that this gives a new and more direct derivation of the generating function of energy changes in a bath, or baths. As found previously, this generating function is given by a Feynman-Vernon-like influence functional, with only time shifts in the kernels coupling the forward and backward paths. We further show that the new approach extends to an-harmonic and possible non-equilibrium baths, provided that the interactions are bi-linear, and that the baths do not interact between themselves. Such baths are characterized by non-trivial cumulants. Every non-zero cumulant of certain environment correlation functions is thus a kernel in a higher-order term in the Feynman-Vernon action.
16.	Aurell, Erik, et al. (författare) Boundary layers in stochastic thermodynamics 2012 Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : American Physical Society. - 1539-3755 .- 1550-2376. ; 85:2, s. 020103- Tidskriftsartikel (refereegranskat)abstract We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give an alternative interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).
17.	Aurell, Erik, et al. (författare) Causal analysis, Correlation-Response, and Dynamic cavity 2016 Ingår i: International Meeting on High-Dimensional Data-Driven Science (HD3-2015). - : Institute of Physics (IOP). Konferensbidrag (refereegranskat)abstract The purpose of this note is to point out analogies between causal analysis in statistics and the correlation-response theory in statistical physics. It is further shown that for some systems the dynamic cavity offers a way to compute the stationary state of a non-equilibrium process effectively, which could then be taken an alternative starting point of causal analysis.
18.	Aurell, Erik, et al. (författare) Cavity master equation for the continuous time dynamics of discrete-spin models 2017 Ingår i: Physical review. E. - : AMER PHYSICAL SOC. - 2470-0045 .- 2470-0053. ; 95:5 Tidskriftsartikel (refereegranskat)abstract We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.
19.	Aurell, Erik (författare) Characteristic functions of quantum heat with baths at different temperatures 2018 Ingår i: Physical review. E. - : AMER PHYSICAL SOC. - 2470-0045 .- 2470-0053. ; 97:6 Tidskriftsartikel (refereegranskat)abstract This paper is about quantum heat defined as the change in energy of a bath during a process. The presentation takes into account recent developments in classical strong-coupling thermodynamics and addresses a version of quantum heat that satisfies quantum-classical correspondence. The characteristic function and the full counting statistics of quantum heat are shown to be formally similar. The paper further shows that the method can be extended to more than one bath, e.g., two baths at different temperatures, which opens up the prospect of studying correlations and heat flow. The paper extends earlier results on the expected quantum heat in the setting of one bath [E. Aurell and R. Eichhorn, New .J Phys. 17, 065007 (2015); E. Aurell, Entropy 19, 595 (2017)].
20.	Aurell, Erik, et al. (författare) Comparing Beliefs, Surveys and Random Walks 2005 Ingår i: Advances in Neural Information Processing Systems 17. - : Morgan Kaufmann Publishers. - 9780262195348 - 0262195348 Konferensbidrag (refereegranskat)abstract Survey propagation is a powerful technique from statistical physics that has been applied to solve the 3-SAT problem both in principle and in practice. We give, using only probability arguments, a common derivation of survey propagation, belief propagation and several interesting hybrid methods. We then present numerical experiments which use WSAT (a widely used random-walk based SAT solver) to quantify the complexity of the 3-SAT formulae as a function of their parameters, both as randomly generated and after simplification, guided by survey propagation. Some properties of WSAT which have not previously been reported make it an ideal tool for this purpose - its mean cost is proportional to the number of variables in the formula (at a fixed ratio of clauses to variables) in the easy-SAT regime and slightly beyond, and its behavior in the hard- SAT regime appears to refiect the underlying structure of the solution space that has been predicted by replica symmetry-breaking arguments. An analysis of the tradeoffs between the various methods of search for satisfying assignments shows WSAT to be far more powerful than has been appreciated, and suggests some interesting new directions for practical algorithm development.
21.	Aurell, Erik, et al. (författare) Diffusion of a Brownian ellipsoid in a force field 2016 Ingår i: Europhysics letters. - : IOP Publishing. - 0295-5075 .- 1286-4854. ; 114:3 Tidskriftsartikel (refereegranskat)abstract We calculate the effective long-term convective velocity and dispersive motion of an ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external force. This long-term motion results as a "net" average behavior from the particle rotation and translation on short time scales. Accordingly, we apply a systematic multi-scale technique to derive the effective equations of motion valid on long times. We verify our theoretical results by comparing them to numerical simulations.
22.	Aurell, Erik, et al. (författare) Dynamic mean-field and cavity methods for diluted Ising systems 2012 Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755 .- 1550-2376. ; 85:3, s. 031119- Tidskriftsartikel (refereegranskat)abstract We compare dynamic mean-field and dynamic cavity methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and we compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks, the dynamic cavity method generally predicts magnetizations of individual spins better than both first-order ("naive") and second-order ("TAP") dynamic mean-field theory.
23.	Aurell, Erik, et al. (författare) Dynamics and performance of susceptibility propagation on synthetic data 2010 Ingår i: European Physical Journal B. - : Springer Science and Business Media LLC. - 1434-6028 .- 1434-6036. ; 77:4, s. 587-595 Tidskriftsartikel (refereegranskat)abstract We study the performance and convergence properties of the susceptibility propagation (SusP) algorithm for solving the Inverse Ising problem. We first study how the temperature parameter (T) in a Sherrington-Kirkpatrick model generating the data influences the performance and convergence of the algorithm. We find that at the high temperature regime (T > 4), the algorithm performs well and its quality is only limited by the quality of the supplied data. In the low temperature regime (T < 4), we find that the algorithm typically does not converge, yielding diverging values for the couplings. However, we show that by stopping the algorithm at the right time before divergence becomes serious, good reconstruction can be achieved down to T a parts per thousand 2. We then show that dense connectivity, loopiness of the connectivity, and high absolute magnetization all have deteriorating effects on the performance of the algorithm. When absolute magnetization is high, we show that other methods can be work better than SusP. Finally, we show that for neural data with high absolute magnetization, SusP performs less well than TAP inversion.
24.	Aurell, Erik, et al. (författare) Epigenetics as a first exit problem 2002 Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 88:4 Tidskriftsartikel (refereegranskat)abstract We develop a framework to discuss the stability of epigenetic states as first exit problems in dynamical systems with noise. We consider in particular the stability of the lysogenic state of the A prophage. The formalism defines a quantitative measure of robustness of inherited states.
25.	Aurell, Erik, et al. (författare) Exploring the diluted ferromagnetic p-spin model with a cavity master equation 2018 Ingår i: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 97:5 Tidskriftsartikel (refereegranskat)abstract We introduce an alternative solution to Glauber multispin dynamics on random graphs. The solution is based on the recently introduced cavity master equation (CME), a time-closure turning the, in principle, exact dynamic cavity method into a practical method of analysis and of fast simulation. Running CME once is of comparable computational complexity as one Monte Carlo run on the same problem. We show that CME correctly models the ferromagnetic p-spin Glauber dynamics from high temperatures down to and below the spinoidal transition. We also show that CME allows an alternative exploration of the low-temperature spin-glass phase of the model.
26.	Aurell, Erik, et al. (författare) Frohlich-coupled qubits interacting with fermionic baths 2020 Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - : AMER PHYSICAL SOC. - 1539-3755 .- 1550-2376. ; 102:1 Tidskriftsartikel (refereegranskat)abstract We consider a quantum system such as a qubit, interacting with a bath of fermions as in the Frohlich polaron model. The interaction Hamiltonian is thus linear in the system variable and quadratic in the fermions. Using the recently developed extension of Feynman-Vernon theory to nonharmonic baths we evaluate quadratic and the quartic terms in the influence action. We find that for this model the quartic term vanish by symmetry arguments. Although the influence of the bath on the system is of the same form as from bosonic harmonic oscillators up to effects to sixth order in the system-bath interaction, the temperature dependence is nevertheless rather different, unless rather contrived models are considered.
27.	Aurell, Erik, et al. (författare) Gaussian belief with dynamic data and in dynamic network 2009 Ingår i: Europhysics letters. - : IOP Publishing. - 0295-5075 .- 1286-4854. ; 87:6 Tidskriftsartikel (refereegranskat)abstract In this paper we analyze Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol (Consensus Propagation, Moallemi C. C. and Van Roy B., IEEE Trans. Inf. Theory, 52 (2006) 4753) where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averaged fluctuate ("dynamic data"), convergence and accuracy are determined by the spectral properties of an associated Ruelle-Perron-Frobenius operator. For Gaussian models on Erdos-Renyi graphs, numerical computation points to a spectral gap remaining in the large- size limit, implying exceptionally good scalability. In a model where the underlying network also fluctuates ("dynamic network"), averaging is more effective than in the dynamic data case. Altogether, this implies very good performance of these methods in very large systems, and opens a new field of statistical physics of large (and dynamic) information systems.
28.	Aurell, Erik, et al. (författare) GENFUNK 2002. - 1 Rapport (övrigt vetenskapligt/konstnärligt)abstract This document summarizes the results obtained by SICS in project GENFUNK (2001). The project was carried out in collaboration with Global Genomics AB (Stockholm, Sweden). Jointly obtained results will be presented separately. Main funding was provided by Swedish Research Agency VINNOVA. Project GENFUNK studied a novel approach of measuring the global gene expression. In the method, mRNA is extracted from a tissue sample and transformed into cDNA captured on magnetic beads. This is then acted on by type IIS restriction endonucleases, which recognize certain short DNA sequences and cut the DNA close to those sequences. The resulting fragments are amplified in PCR with selected ligation fragments, and displayed in capillary electrophoresis. Determining the gene expression levels from the peak data is combinatorial optimization problem, which can in principle be solved, to give expression levels of most genes active in sampled cells, with good accuracy.
29.	Aurell, Erik (författare) Global Estimates of Errors in Quantum Computation by the Feynman-Vernon Formalism 2018 Ingår i: Journal of statistical physics. - : SPRINGER. - 0022-4715 .- 1572-9613. ; 171:5, s. 745-767 Tidskriftsartikel (refereegranskat)abstract The operation of a quantum computer is considered as a general quantum operation on a mixed state on many qubits followed by a measurement. The general quantum operation is further represented as a Feynman-Vernon double path integral over the histories of the qubits and of an environment, and afterward tracing out the environment. The qubit histories are taken to be paths on the two-sphere as in Klauder's coherent-state path integral of spin, and the environment is assumed to consist of harmonic oscillators initially in thermal equilibrium, and linearly coupled to to qubit operators . The environment can then be integrated out to give a Feynman-Vernon influence action coupling the forward and backward histories of the qubits. This representation allows to derive in a simple way estimates that the total error of operation of a quantum computer without error correction scales linearly with the number of qubits and the time of operation. It also allows to discuss Kitaev's toric code interacting with an environment in the same manner.
30.	Aurell, Erik, et al. (författare) Growth optimal investment and pricing of derivatives 2000 Ingår i: Physica A. - 0378-4371 .- 1873-2119. ; 280:04-mar, s. 505-521 Tidskriftsartikel (refereegranskat)abstract We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. tinder the assumptions of no trading costs, and no restrictions on lending, we find an appropriate equivalent martingale measure that prices the underlying and the derivative security. We compare our result with other alternative pricing procedures in the literature, and discuss the limits of validity of the lognormal approximation. We also generalize the pricing method to a market with correlated stocks. The expected estimation error of the optimal investment fraction is derived in a closed form, and its validity is checked with a small-scale empirical test.
31.	Aurell, Erik, et al. (författare) Growth-Optimal Strategies with Quadratic Friction Over Finite-Time Investment Horizons 2004 Ingår i: International Journal of Theoretical and Applied Finance. - 0219-0249. ; 7:5, s. 645-657 Tidskriftsartikel (refereegranskat)abstract We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of capital invested in stocks within an interval around an ideal optimal investment. The size of the holding interval is determined by the intensity of the transaction costs and the time horizon.
32.	Aurell, Erik, et al. (författare) Hawking radiation and the quantum marginal problem 2022 Ingår i: Journal of Cosmology and Astroparticle Physics. - : IOP Publishing. - 1475-7516. ; :1 Tidskriftsartikel (refereegranskat)abstract In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate. The problem of the fate of information in this process is known as the "black hole information paradox". Two main types of resolution postulate either a fundamental loss of information in Nature - hence the breakdown of quantum mechanics - or some sort of new physics, e.g. quantum gravity, which guarantee the global preservation of unitarity. Here we explore the second possibility with the help of recent developments in continuous-variable quantum information. Concretely, we employ the solution to the Gaussian quantum marginal problem to show that the thermality of all individual Hawking modes is consistent with a global pure state of the radiation. Surprisingly, we find out that the mods of radiation of an astrophysical black hole are thermal until the very last burst. In contrast, the single-mode thermality of Hawking radiation originating from microscopic black holes, expected to evaporate through several quanta, is not excluded, though there are constraints on modes' frequencies. Our result paves the way towards a systematic study of multi-mode correlations in Hawking radiation.
33.	Aurell, Erik, et al. (författare) Inverse Ising Inference Using All the Data 2012 Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 108:9, s. 090201- Tidskriftsartikel (refereegranskat)abstract We show that a method based on logistic regression, using all the data, solves the inverse Ising problem far better than mean-field calculations relying only on sample pairwise correlation functions, while still computationally feasible for hundreds of nodes. The largest improvement in reconstruction occurs for strong interactions. Using two examples, a diluted Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that interaction topologies can be recovered from few samples with good accuracy and that the use of l(1) regularization is beneficial in this process, pushing inference abilities further into low-temperature regimes.
34.	Aurell, Erik, et al. (författare) Large deviations and fluctuation theorem for the quantum heat current in the spin-boson model 2020 Ingår i: Physical review. E. - : American Physical Society (APS). - 2470-0045 .- 2470-0053. ; 101:5 Tidskriftsartikel (refereegranskat)abstract We study the heat current flowing between two baths consisting of harmonic oscillators interacting with a qubit through a spin-boson coupling. An explicit expression for the generating function of the total heat flowing between the right and left baths is derived by evaluating the corresponding Feynman-Vernon path integral by performing the noninteracting blip approximation (NIBA). We recover the known expression, obtained by using the polaron transform. This generating function satisfies the Gallavotti-Cohen fluctuation theorem, both before and after performing the NIBA. We also verify that the heat conductance is proportional to the variance of the heat current, retrieving the well-known fluctuation dissipation relation. Finally, we present numerical results for the heat current.
35.	Aurell, Erik, et al. (författare) Non-linear regime of the gravitational instability 2005 Ingår i: Proceedings of Frontiers of Nonlinear Physics. ; , s. 619-629 Konferensbidrag (refereegranskat)
36.	Aurell, Erik, et al. (författare) On the dynamics of a self-gravitating medium with random and non-random initial conditions 2001 Ingår i: Physica D. - 0167-2789 .- 1872-8022. ; 148:04-mar, s. 272-288 Tidskriftsartikel (refereegranskat)abstract The dynamics of a 1D self-gravitating medium with initial density almost uniform is studied. Numerical experiments are performed with ordered and with Gaussian random initial conditions. The phase space portraits art shown to be qualitatively similar to shock waves, in particular with initial conditions of Brownian type. The PDF of the mass distribution is investigated.
37.	Aurell, Erik, et al. (författare) On the von Neumann entropy of a bath linearly coupled to a driven quantum system 2015 Ingår i: New Journal of Physics. - : IOP Publishing. - 1367-2630. ; 17 Tidskriftsartikel (refereegranskat)abstract The change of the von Neumann entropy of a set of harmonic oscillators initially in thermal equilibrium and interacting linearly with an externally driven quantum system is computed by adapting the Feynman-Vernon influence functional formalism. This quantum entropy production has the form of the expectation value of three functionals of the forward and backward paths describing the system history in the Feynman-Vernon theory. In the classical limit of Kramers-Langevin dynamics (Caldeira-Leggett model) these functionals combine to three terms, where the first is the entropy production functional of stochastic thermodynamics, the classical work done by the system on the environment in units of k(B)T, and the second and the third other functionals which have no analogue in stochastic thermodynamics.
38.	Aurell, Erik (författare) On Work and Heat in Time-Dependent Strong Coupling 2017 Ingår i: Entropy. - : MDPI. - 1099-4300. ; 19:11 Tidskriftsartikel (refereegranskat)abstract This paper revisits the classical problem of representing a thermal bath interacting with a system as a large collection of harmonic oscillators initially in thermal equilibrium. As is well known, the system then obeys an equation, which in the bulk and in the suitable limit tends to the Kramers-Langevin equation of physical kinetics. I consider time-dependent system-bath coupling and show that this leads to an additional harmonic force acting on the system. When the coupling is switched on and switched off rapidly, the force has delta-function support at the initial and final time. I further show that the work and heat functionals as recently defined in stochastic thermodynamics at strong coupling contain additional terms depending on the time derivative of the system-bath coupling. I discuss these terms and show that while they can be very large if the system-bath coupling changes quickly, they only give a finite contribution to the work that enters in Jarzynski's equality. I also discuss that these corrections to standard work and heat functionals provide an explanation for non-standard terms in the change of the von Neumann entropy of a quantum bath interacting with a quantum system found in an earlier contribution (Aurell and Eichhorn, 2015).
39.	Aurell, Erik, et al. (författare) Optimal hedging of derivatives with transaction costs 2006 Ingår i: International Journal of Theoretical and Applied Finance. - 0219-0249. ; 9:7, s. 1051-1069 Tidskriftsartikel (refereegranskat)abstract We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton-Bellman-Jacobi equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at hand, these conditions simply imply arbitrage-free ("Black-Scholes") pricing of the derivative. While pricing is hence not changed by friction allow a portfolio to fluctuate around a delta hedge. In the limit of weak friction, we determine the optimal control to essentially be of two parts: a strong control, which tries to bring the stock-and-derivative portfolio towards a Black-Scholes delta hedge; and a weak control, which moves the portfolio by adding or subtracting a Black-Scholes hedge. For simplicity we assume growth-optimal investment criteria and quadratic friction.
40.	Aurell, Erik, et al. (författare) Optimal Protocols and Optimal Transport in Stochastic Thermodynamics 2011 Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 106:25, s. 250601- Tidskriftsartikel (refereegranskat)abstract Thermodynamics of small systems has become an important field of statistical physics. Such systems are driven out of equilibrium by a control, and the question is naturally posed how such a control can be optimized. We show that optimization problems in small system thermodynamics are solved by (deterministic) optimal transport, for which very efficient numerical methods have been developed, and of which there are applications in cosmology, fluid mechanics, logistics, and many other fields. We show, in particular, that minimizing expected heat released or work done during a nonequilibrium transition in finite time is solved by the Burgers equation and mass transport by the Burgers velocity field. Our contribution hence considerably extends the range of solvable optimization problems in small system thermodynamics.
41.	Aurell, Erik, et al. (författare) Quantum Black Holes as Solvents 2021 Ingår i: Foundations of physics. - : Springer Nature. - 0015-9018 .- 1572-9516. ; 51:2 Tidskriftsartikel (refereegranskat)abstract Almost all of the entropy in the universe is in the form of Bekenstein-Hawking (BH) entropy of super-massive black holes. This entropy, if it satisfies Boltzmann's equation S=log N, hence represents almost all the accessible phase space of the Universe, somehow associated to objects which themselves fill out a very small fraction of ordinary three-dimensional space. Although time scales are very long, it is believed that black holes will eventually evaporate by emitting Hawking radiation, which is thermal when counted mode by mode. A pure quantum state collapsing to a black hole will hence eventually re-emerge as a state with strictly positive entropy, which constitutes the famous black hole information paradox. Expanding on a remark by Hawking we posit that BH entropy is a thermodynamic entropy, which must be distinguished from information-theoretic entropy. The paradox can then be explained by information return in Hawking radiation. The novel perspective advanced here is that if BH entropy counts the number of accessible physical states in a quantum black hole, then the paradox can be seen as an instance of the fundamental problem of statistical mechanics. We suggest a specific analogy to the increase of the entropy in a solvation process. We further show that the huge phase volume (N), which must be made available to the universe in a gravitational collapse, cannot originate from the entanglement between ordinary matter and/or radiation inside and outside the black hole. We argue that, instead, the quantum degrees of freedom of the gravitational field must get activated near the singularity, resulting in a final state of the 'entangled entanglement' form involving both matter and gravity.
42.	Aurell, Erik, et al. (författare) Random Pure Gaussian States and Hawking Radiation 2024 Ingår i: Physical Review Letters. - : American Physical Society (APS). - 0031-9007 .- 1079-7114. ; 133:6 Tidskriftsartikel (refereegranskat)abstract A black hole evaporates by Hawking radiation. Each mode of that radiation is thermal. If the total state is nevertheless to be pure, modes must be entangled. Estimating the minimum size of this entanglement has been an important outstanding issue. We develop a new theory of constrained random symplectic transformations, based on the assumptions that the total state is pure and Gaussian with given marginals. In the random constrained symplectic model we then compute the distribution of mode-mode correlations, from which we bound mode-mode entanglement. Modes of frequency much larger than [k(B)T(H)(t)/h] are not populated at time t and drop out of the analysis. Among other relatively thinly populated modes (earlytime high-frequency modes and/or late modes of any frequency), we find correlations and hence entanglement to be strongly suppressed. Relatively highly populated modes (early-time low-frequency modes) can, on the other hand, be strongly correlated, but a detailed analysis reveals that they are nevertheless very unlikely to be entangled. Our analysis hence establishes that restoring unitarity after a complete evaporation of a black hole does not require any significant quantum entanglement between any pair of Hawking modes. Our analysis further gives exact general expressions for the distribution of modemode correlations in random, pure, Gaussian states with given marginals, which may have applications beyond black hole physics.
43.	Aurell, Erik, et al. (författare) Real-time dynamics in diluted quantum networks 2022 Ingår i: Physical Review A: covering atomic, molecular, and optical physics and quantum information. - : AMER PHYSICAL SOC. - 2469-9926 .- 2469-9934. ; 105:2 Tidskriftsartikel (refereegranskat)abstract We introduce an approach to characterize the dynamics of disordered quantum networks. Each quantum element (i.e., each node) of the network experiences the other nodes as an effective environment that can be self-consistently represented by a Feynman-Vernon influence functional. For networks having the topology of locally treelike graphs, these Feynman-Vernon (FV) functionals can be determined by a new version of the cavity or belief propagation (BP) method. Here, we find the fixed point solution of this version of BP for a network of uniform quantum harmonic oscillators. Then, we estimate the effects of the disorder in these networks within the replica symmetry ansatz. We show that over a large time interval, at small disorder, the real part of the FV functional induces decoherence and classicality while at sufficiently large disorder the Feynman-Vernon functional tends to zero and the coherence survives, signaling in a time setting, the onset of an Anderson's transition.
44.	Aurell, Erik, et al. (författare) Refined Second Law of Thermodynamics for Fast Random Processes 2012 Ingår i: Journal of statistical physics. - : Springer Science and Business Media LLC. - 0022-4715 .- 1572-9613. ; 147:3, s. 487-505 Tidskriftsartikel (refereegranskat)abstract We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based on the Monge-Kantorovich optimal mass transport and becomes relevant for processes far from quasi-stationary regime. General discussion is illustrated by numerical analysis of the optimal memory erasure protocol for a model for micron-size particle manipulated by optical tweezers.
45.	Aurell, Erik, et al. (författare) Self-gravitating systems in a three-dimensional expanding universe 2002. - 1 Ingår i: European journal of physics. - 0143-0807 .- 1361-6404. Tidskriftsartikel (refereegranskat)abstract The non-linear evolution of one-dimensional perturbations in a three-dimensional expanding Universe is considered. A general Lagrangian scheme is derived, and compared to two previously introduced approximate models. These models are simulated with heap-based event-driven numerical procedure that allows for the study of large systems, averaged over many realisations of random initial conditions. One of the models is shown to be qualitatively, and, in some respects, concerning mass aggregation, quantitatively similar to the adhesion model.
46.	Aurell, Erik, et al. (författare) Stability puzzles in phage lambda 2002 Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1063-651X .- 1095-3787. ; 65:5 Tidskriftsartikel (refereegranskat)abstract In the absence of RecA-mediated cleavage of the repressor, the X prophage is exceptionally stable. We. develop a stochastic model that predicts the stability of such epigenetic states from affinities of the molecular components. We find that the stability, in particular, depends on the maximum possible cI protein production. and on the number of translated cro proteins per transcribed mRNA. We apply the model to the behavior of recently published mutants of O-R and find, in particular, that a mutant that overexpress cro behaves in a different way than what was predicted, thus suggesting that the current view of the O-R switch is incomplete. The approach described here should be generally applicable to the stability of expressed states.
47.	Aurell, Erik, et al. (författare) Steady diffusion in a drift field : A comparison of large-deviation techniques and multiple-scale analysis 2017 Ingår i: Physical review. E. - : AMER PHYSICAL SOC. - 2470-0045 .- 2470-0053. ; 96:3 Tidskriftsartikel (refereegranskat)abstract A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while the effective diffusion has two terms. One is of the equilibrium type and satisfies an Einstein relation with the effective mobility while the other is quadratic in the applied force. In this contribution we present two new methods to obtain these results, on the one hand using large deviation techniques and on the other by a multiple-scale analysis, and compare the two. We consider both systems with discrete internal states and continuous internal states. We show that the auxiliary equations in the multiple-scale analysis can also be derived in second-order perturbation theory in a large deviation theory of a generating function (discrete internal states) or generating functional (continuous internal states). We discuss that measuring the two components of the effective diffusion give a way to determine kinetic rates from only first and second moments of the displacement in steady state.
48.	Aurell, Erik, 1961-, et al. (författare) The bulk and the tail of minimal absent words in genome sequences 2016 Ingår i: Physical Biology. - : Institute of Physics (IOP). - 1478-3967 .- 1478-3975. ; 13:2 Tidskriftsartikel (refereegranskat)abstract Minimal absent words (MAW) of a genomic sequence are subsequences that are absent themselves but the subwords of which are all present in the sequence. The characteristic distribution of genomic MAWs as a function of their length has been observed to be qualitatively similar for all living organisms, the bulk being rather short, and only relatively few being long. It has been an open issue whether the reason behind this phenomenon is statistical or reflects a biological mechanism, and what biological information is contained in absent words. % In this work we demonstrate that the bulk can be described by a probabilistic model of sampling words from random sequences, while the tail of long MAWs is of biological origin. We introduce the novel concept of a core of a minimal absent word, which are sequences present in the genome and closest to a given MAW. We show that in bacteria and yeast the cores of the longest MAWs, which exist in two or more copies, are located in highly conserved regions the most prominent example being ribosomal RNAs (rRNAs). We also show that while the distribution of the cores of long MAWs is roughly uniform over these genomes on a coarse-grained level, on a more detailed level it is strongly enhanced in 3' untranslated regions (UTRs) and, to a lesser extent, also in 5' UTRs. This indicates that MAWs and associated MAW cores correspond to fine-tuned evolutionary relationships, and suggest that they can be more widely used as markers for genomic complexity.
49.	Aurell, Erik, et al. (författare) The inner structure of Zeldovich pancakes 2003 Ingår i: Physica D. - : Elsevier BV. - 0167-2789 .- 1872-8022. ; 186:04-mar, s. 171-184 Tidskriftsartikel (refereegranskat)abstract The evolution of a planar perturbation in a Einstein-de Sitter Universe is studied using a previously introduced Lagrangian scheme. An approximate discrete dynamical system is derived, which describes the mass agglomeration process. Quantitative predictions for the late-time mean density profile are obtained therefrom, and validated by numerical simulations. A simple but important result is that the characteristic scale of a mass agglomeration is an increasing function of cosmological time t. For one kind of initial conditions we further find a scaling regime for the density profile of a collapsing object. These results are compared with analogous investigations for the adhesion model (Burgers equation with positive viscosity). We further study the mutual motion of two mass agglomerations, and show that they oscillate around each other for long times, like two heavy particles. Individual particles in the two agglomerations do not mix effectively on the time scale of the inter-agglomeration motion.
50.	Aurell, Erik (författare) The Maximum Entropy Fallacy Redux? 2016 Ingår i: PloS Computational Biology. - : Public Library of Science (PLoS). - 1553-734X .- 1553-7358. ; 12:5 Tidskriftsartikel (refereegranskat)

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