Spin Glasses

Magnetite nanostructured powder samples were synthesized by aging chemical method. Phase, structural, and magnetic properties were characterized. X-ray diffraction patterns showed cubic magnetite pure phase, with average crystallite size, 〈D〉, equal to 40 nm. Susceptibility measurements showed the well-known Verwey transition at a temperature of 90 K. The decrease of Verwey transition temperature, with respect to the one reported in literature (125 K) was attributed to the low average crystallite size. Moreover, the spin-glass like transition was observed at 35 K. Activation energy calculated from susceptibility curves, with values ranging from 6.26 to 6.93 meV, showed a dependence of spin-glass transition on frequency. Finally, hysteresis loops showed that there is not an effect of Verwey transition on magnetic properties. On the other hand, a large increase of coercivity and remanent magnetization at a temperature between 5 and 50 K confirmed the presence of a magnetic transition at low temperatures.

We report the magnetic characterization of the Cr-doped layered dichalcogenide TiSe 2. The temperature dependent magnetic susceptibilities are typical of those seen in geometrically frustrated insulating antiferromagnets. The Cr moment is close to the spin-only value, and the Curie−Weiss temperatures (θ cw) are between −90 and −230 K. Freezing of the spin system, which is glassy, characterized by peaks in the ac and dc susceptibility and specific heat, does not occur until below T/θ cw = 0.05. The CDW transition seen in the resistivity for pure TiSe 2 is still present for 3% Cr substitution but is absent by 10% substitution, above which the materials are metallic and p-type. Structural refinements, magnetic characterization , and chemical considerations indicate that the materials are of the type Ti 1−x Cr x Se 2‑x/2 for 0 ≤ x ≤ 0.6. ■ INTRODUCTION Frustration of magnetic ordering arises in both atomically disordered systems and systems where the magnetic interactions are not compatible with the underlying structural symmetry. 1−5 Classical spin glasses and systems with magnetic ions on triangular or tetrahedral lattices display such frustration. The most-often-studied materials with strong geometric magnetic frustration are electrically insulating or at best strongly semiconducting, 5−16 and classical spin glass systems can be either metallic or semiconducting. 17 Typically, frustrated magnetic materials are characterized by a Curie−Weiss theta θ cw that is significantly greater than the spin freezing temperature T f. The frustration index f = θ cw /T f is often taken as a general characterization of the degree of frustration. The MX 2 layered transition-metal dichalcogenides (TMDCs, M = Mo, W, V, Nb, Ta, Ti, Zr, Hf, and Re, and X = Se, S, or Te) are a large family of solids with layered triangular metal lattices and have long been of interest due to the rich electronic properties that arise from their low dimensionality (see, e.g. refs 18−22). Within the TMDCs, 1T-TiSe 2 has attracted special attention due to the presence of a Charge Density Wave (CDW) that onsets at 200 K. 22,23 The material has trigonal symmetry, 24 with TiSe 6 octahedra sharing edges in triangular geometry TiSe 2 layers that are bonded to each other by Se−Se van der Waals forces (Figure 1a). Here we study the effect of Cr substitution for Ti in 1T-TiSe 2. We find that as Cr atoms are substituted for Ti, they induce metal occupancy in the van der Waals gap between the TiSe 2 layers (Figure 1a). We interpret our data to indicate that at concentrations less than about 20%, the Cr ions primarily occupy the interstitial octahedral sites in the van der Waals layers, but at higher concentrations they occupy both the octahedral interstitial sites and sites in the Ti layers; when they do that they then displace some Ti into the interstitial positions and the system becomes quite disordered. (The materials system is complex: previous studies 25,26 of Cr-intercalated TiSe 2 yielded magnetic properties that are significantly different from those that are observed here, implying that the magnetic behavior of the system may be dependent on synthetic conditions.) Cr ions most frequently are ionic and have the oxidation state Cr 3+ in solids due to their very strong Hunds-rule coupling. 27 In a material like TiSe 2 , which is a small band gap semiconductor with a conduction band made from empty Ti d states and a valence band made from filled Se p states (i.e., consisting of Ti 4+ and Se 2−), the presence of Cr 3+ along with Ti 4+ and Se 2− requires a decrease in the Se to metal ratio to below 2:1 and a formula Ti 1−x Cr x Se 2‑x/2 to maintain charge neutrality. Our XPS analysis supports these formal oxidation state assignments. This picture for Cr-doped TiSe 2 is further supported by the materials synthesis, the diffraction data, the magnetic data, and the presence of two types of magnetic spins clearly seen in the ac susceptibility for higher x materials. The DC magnetic susceptibilities confirm that the Cr moments in Ti 1−x Cr x Se 2‑x/2 are within experimental error of the expected Cr 3+ spin-only value. 28 The antiferromagnetic Curie−Weiss temperatures are large, between −90 and −230 K. The freezing

We propose the binding information as an information theoretic measure of complexity between multiple random variables, such as those found in the Ising or Potts models of interacting spins, and compare it with several previously proposed measures of statistical complexity, including excess entropy, Bialek et al 's predictive information, and the multi-information. We discuss and prove some of the properties of binding information, particularly in relation to multi-information and entropy, and show that, in the case of binary random variables interactions, the processes which maximise binding information are the 'parity' processes. The computation of binding information is demonstrated on Ising models of finite spin systems, showing that various upper and lower bounds are respected and also that there is a strong relationship between the introduction of high-order interactions and an increase of binding-information. Finally we discuss some of the implications this has for the use of the binding information as a measure of complexity.

Magnetic phase transitions in the rare-earth intermetallic compound Nd 5 Ge 3 have been investigated using a single crystal. Magnetic measurements confirm that Nd 5 Ge 3 is in the antiferromagentic state below T N ¼ 51 K, in literature. An irreversible magnetic-field-induced antiferromagentic to ferromagnetic transition has been found below T t ¼ 26 K. In this state, a metamagnetic transition takes place in the first magnetizing process; a ferromagnetic state having a remanent magnetization M R is stabilized after removing the external magnetic field. M R does not show noticeable relaxation behavior and a rectangular-type hysteresis loop is maintained in the following magnetization process. As origin of the irreversibility, a martensitic structural phase transition under the external field can be considered. The magnetic-field cooling effect on the magnetic susceptibility indicates the coexistence of a kind of spinglass state with long-range antiferromagnetic ordering.

We report the bulk magnetic properties of a yet unexplored vanadium-based multi-valenced
spinel system, Zn3V3O8. A Curie–Weiss fit of our dc magnetic susceptibility χ(T ) data
in the temperature region of 140–300K yields a Curie constant C = 0.75 cm3Kmole−1 V−1,
θCW = −370 K. We have observed a splitting between the zero field cooled (ZFC) and
field cooled (FC) susceptibility curves below a temperature Tirr of about 6.3K. The value of
the ‘frustration parameter’ ( |θCW|
TN
∼ 100) suggests that the system is strongly frustrated. From
the ac susceptibility measurements we find a logarithmic variation of freezing temperature (Tf )
with frequency ν attesting to the formation of a spin glass below Tf . However, the value of the
characteristic frequency obtained from the Vogel–Fulcher fit suggests that the ground state is
closer to a cluster glass rather than a conventional spin glass. We explored further consequences
of the spin glass behavior and observed aging phenomena and memory effect (both in ZFC and
FC).We found that a positive temperature cycle erases the memory, as predicted by the hierarchical
model. From the heat capacityCP data, a hump-like anomalywas observed inCP /T at about
3.75 K. Below this temperature the magnetic heat capacity shows a nearly linear dependence
with T which is consistent with the formation of a spin glass state below Tf in Zn3V3O8.

Research Program Outline: Technophysics: The Formal Study of Smart Networks and Complex System Criticality

The aim of this research program is to formalize research regarding technophysics (the application of physics to the study of technology) and smart networks (intelligent autonomously-operating networks), particularly in the areas of study proposed in this research agenda.

Thepreparation andproperties of NbjO, coatings made bythesol-gel process were investigated. Thefilms were deposited byspincoating on In203:Snlglass and quartz substrates from a polymeric solutions of niobia derived from niobium ethoxide. The films were characterized byinvestigation ofthestoichiometry.refractive index, optical transmission, electrochemical behavior. andthemicrostructure. X-ray diffraction studies showed the films to be amorphous forheat treatments below 450°C. X-ray photoelectron spectroscopy (XPS) measurement revealed theO:Nbatomic stoichiometry tobe5:2. Cyclic voltammetric measurements showed thattheNb 20S / 1M LiClOcpropylene carbonate system exhibits electrochemical reversibility beyond I 200 cycles without change in performance. In situ UV-Vis-NIR spectroelectrochemical measurement revealed that Nb 2 0 s films exhibit an electrochromic effect in the spectral range 300<A<2100 nm and remain unchanged in the infrared spectral range. The change in visible transmittance was 40% for a 250nm thick electrode. XPS spectra indicate thatNb(V) is reduced to a lower valence state Nb(IV) in a colored state with injected Li ". The bronze coloration is due to a simultaneous injection of electrons and Li + ions into Nb 20S ' The sol-gel-deposited Nb 20S films are useful for cathodically coloring electrochromic electrodes in electrochromic devices.

Magnetite nanostructured powder samples were synthesized by aging chemical method. Phase, structural, and magnetic properties were characterized. X-ray diffraction patterns showed cubic magnetite pure phase, with average crystallite size, hDi, equal to 40 nm. Susceptibility measurements showed the well-known Verwey transition at a temperature of 90 K. The decrease of Verwey transition temperature, with respect to the one reported in literature (125 K) was attributed to the low average crystallite size. Moreover, the spin-glass like transition was observed at 35 K. Activation energy calculated from susceptibility curves, with values ranging from 6.26 to 6.93 meV, showed a dependence of spin-glass transition on frequency. Finally, hysteresis loops showed that there is not an effect of Verwey transition on magnetic properties. On the other hand, a large increase of coercivity and remanent magnetization at a temperature between 5 and 50 K confirmed the presence of a magnetic transition at low temperatures. V C 2013 American Institute of Physics. [http://dx.

We propose an efficient Monte Carlo algorithm for simulating a "hardlyrelaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replica is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional ±J Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multicanonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.

Nanosized mixed valent perovskite manganites CaMnO 3 , La doped Ca 0.7 La 0.3 MnO 3 (S1) and Ce co-doped Ca 0.7 La 0.3 Mn 0.8 Ce 0.2 O 3 (S2) samples were synthesized by the modified glycine-nitrate procedure. Their magnetic properties were investigated by M(T) measurements in both ZFC and FC regimes in several applied DC magnetic fields, as well as by AC susceptibility measurements. Nanosized CaMnO 3 exhibits similar behavior as its bulk counterpart with the antiferromagnetic transition temperature T N = 120 K. Obtained magnetization curves for S1 and S2 display behavior typical for magnetic nanoparticle systems, such as irreversibility of ZFC and FC curves, and field dependence of the magnetization maximum in ZFC branches. Field dependence of the magnetization maxima (T max versus H 2/3 ) as well as AC susceptibility behavior (frequency dependence of T max ) point to the presence of considerable interparticle interactions. Consequently, below T max the formation of super spin-glass state can be assumed.

In a pioneering work ,  Mézard and Parisi proved that methods from the theory of disordered systems at low temperature can be used to solve very difficult combinatorial optimisation problems, being possible to assign an energy to their configurations and proceed with the usual apparatus of statistical mechanics. Moreover, numerical simulations showed reach behaviors that, as well as being approachable by replica calculations, opened a lot of interesting questions. Among the variety of problems that one can study in this context this work focused on the linear sum assignment problem, which can be described for example as the assignment of n tasks to n workers in such a way that the total time of execution of the tasks is minimum, being known that worker i spends tij seconds to complete the task j. The work was developed in two stages: first it was constructed and tested a C++ implementation of the Jonker-Volgenant algorithm that solves a general linear sum assignment problem; this code was used to study the Euclidean bipartite matching problem in D dimensions, where frustration is imposed by the geometry of the ambient space, and to see how this problem reaches its mean field approximation in the D → ∞limit (the random assignment problem), where the assignment cost is completely aleatory.

This paper presents a method for searching ground states of Ising spin glasses. The Ising model is one of the most commonly used because of its simplicity and its accuracy in representing real problems. We tackle the problem of finding ground states with particle swarm optimization (PSO), a population-based stochastic optimization technique inspired by social behavior of bird flocking. The paper is organized as follows: the first section briefly presents Ising spin glasses. Section 2 describes the basic principles of the particle swarm optimization meta-heuristic. Section 3 presents experimental results, followed by some conclusion and future work in Section 4.

Magnetic phase transitions in the rare-earth intermetallic compound Nd 5Ge 3 have been investigated using a single crystal. Magnetic measurements confirm that Nd 5Ge 3 is in the antiferromagentic state below TN=51 K, in literature. An irreversible magnetic-field-induced antiferromagentic to ferromagnetic transition has been found below Tt=26 K. In this state, a metamagnetic transition takes place in the first magnetizing process; a ferromagnetic state having a remanent magnetization MR is stabilized after removing the external magnetic field. MR does not show noticeable relaxation behavior and a rectangular-type hysteresis loop is maintained in the following magnetization process. As origin of the irreversibility, a martensitic structural phase transition under the external field can be considered. The magnetic-field cooling effect on the magnetic susceptibility indicates the coexistence of a kind of spin-glass state with long-range antiferromagnetic ordering.

To address the incompatibility of Zhang-Rice singlet formation and the observed spin glass behavior, an effective model is proposed for the electronic behavior of cuprate materials. The model includes an antiferromagnetic interaction between the spin of the hole in a Zhang-Rice orbital and the spin of the hole on the corresponding copper site. While in the large interaction limit this recovers the t-J model, in the low energy limit the Zhang-Rice singlets are deformed. It is also shown that such deformation can induce random defect ferromagnetic (FM) bonds between adjacent local spins, an effect herein referred to as unusual double exchange, and then spin glass behavior shall result in the case of localized holes. A derivation of the model is also presented.

In this work we introduce and analyze the stochastic dynamics obeyed by a model of an immune network recently introduced by the authors. We develop Fokker-Planck equations for the single lymphocyte behavior and coarse grained Langevin schemes for the averaged clone behavior. After showing agreement with real systems (as a short path Jerne cascade), we suggest, both with analytical and numerical arguments, explanations for the generation of (metastable) memory cells, improvement of the secondary response (both in the quality and quantity) and bell shaped modulation against infections as a natural behavior. The whole emerges from the model without being postulated a-priori as it often occurs in second generation immune networks: so the aim of the work is to present some out-ofequilibrium features of this model and to highlight mechanisms which can replace a-priori assumptions in view of further detailed analysis in theoretical systemic immunology.

We introduce an information theoretic measure of statistical structure, called 'binding information', for sets of random variables, and compare it with several previously proposed measures including excess entropy, Bialek et al.'s predictive information, and the multi-information. We derive some of the properties of the binding information, particularly in relation to the multi-information, and show that, for finite sets of binary random variables, the processes which maximises binding information are the 'parity' processes. Finally we discuss some of the implications this has for the use of the binding information as a measure of complexity.

Nanosized mixed valent perovskite manganites CaMnO 3 , La doped Ca 0.7 La 0.3 MnO 3 (S1) and Ce co-doped Ca 0.7 La 0.3 Mn 0.8 Ce 0.2 O 3 (S2) samples were synthesized by the modified glycine-nitrate procedure. Their magnetic properties were investigated by M(T) measurements in both ZFC and FC regimes in several applied DC magnetic fields, as well as by AC susceptibility measurements. Nanosized CaMnO 3 exhibits similar behavior as its bulk counterpart with the antiferromagnetic transition temperature T N = 120 K. Obtained magnetization curves for S1 and S2 display behavior typical for magnetic nanoparticle systems, such as irreversibility of ZFC and FC curves, and field dependence of the magnetization maximum in ZFC branches. Field dependence of the magnetization maxima (T max versus H 2/3 ) as well as AC susceptibility behavior (frequency dependence of T max ) point to the presence of considerable interparticle interactions. Consequently, below T max the formation of super spin-glass state can be assumed.

A short review is made of the key magnetic properties of dilute cubic R,Y,-,A& (R =Tb, Dy) intermetallics, in order to show their main magnetic features. Dilution by Y introduces a weak random magnetic anisotropy (RMA). The rich magnetic phase diagram is described, including paramagnetic (P), spin glass (SG), correlated spin glass (CSG), random ferromagnetic (RFM), and ferromagnetic (F) phases, with a triple point and two multicritical ones. The paper deals with the induced macroscopic magnetic anisotropy cooling in a magnetic field below T,, or T,, transition temperatures, which can be either unidirectional or uniaxial or both. High-field (3 Tj magnetostriction in Tb series shows, for x=0.48, 0.59, 0.87, a decrease of the Callen CY exponent (b--m", m=reduced magnetization) below 3. The Sompolinsky irreversibility parameter A has been determined for the Tb series in the SG regime, and a replica model is presented to explain the A(T) dependence. The character of the P-SG or P-CSG transitions is addressed, through the scaling of nonlinear susceptibility (SG regime) or a ferromagnetic-like scaling of magnetization, respectively. From quasielastic neutron scattering around Q= [ 1, 1, l] we determine the temperature dependence of the magnetic correlation length in Dya.sY&l,, which peaks, but does not diverge at T, . A magnon excitation at 3.5 meV is reported for x=0.8.

The distribution of interaction fields of an Ising-like system, obtained by Monte Carlo entropic sampling is used for modeling the hysteretic behavior of patterned media made of magnetic particles with a common anisotropy axis; a variant of the canonical Edwards-Anderson Ising spin glass model is introduced. r

We study the 3d Ising spin glass with ±1 couplings. We introduce a modified local action. We use finite size scaling techniques and very large lattice simulations. We find that our data are compatible both with a finite T transition and with a T = 0 singularity of an unusual type.

All higher-spin (s≥1/2) Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3, exactly on a d=3 hierarchical model and, simultaneously, by the Migdal-Kadanoff approximation on the cubic lattice. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d=3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s→∞. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of  λ=1.93 and runaway exponent of yR=0.24, showing simultaneous strong-chaos and strong-coupling behavior. The ferromagnetic-spin-glass and spin-glass-antiferromagnetic phase transitions occurring, along their whole length, respectively at pt=0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.

Thepreparation andproperties of NbjO, coatings made bythesol-gel process were investigated. Thefilms were deposited byspincoating on In203:Snlglass and quartz substrates from a polymeric solutions of niobia derived from niobium ethoxide. The films were characterized byinvestigation ofthestoichiometry.refractive index, optical transmission, electrochemical behavior. andthemicrostructure. X-ray diffraction studies showed the films to be amorphous forheat treatments below 450°C. X-ray photoelectron spectroscopy (XPS) measurement revealed theO:Nbatomic stoichiometry tobe5:2. Cyclic voltammetric measurements showed thattheNb 20S / 1M LiClOcpropylene carbonate system exhibits electrochemical reversibility beyond I 200 cycles without change in performance. In situ UV-Vis-NIR spectroelectrochemical measurement revealed that Nb 2 0 s films exhibit an electrochromic effect in the spectral range 300<A<2100 nm and remain unchanged in the infrared spectral range. The change in visible transmittance was 40% for a 250nm thick electrode. XPS spectra indicate thatNb(V) is reduced to a lower valence state Nb(IV) in a colored state with injected Li ". The bronze coloration is due to a simultaneous injection of electrons and Li + ions into Nb 20S ' The sol-gel-deposited Nb 20S films are useful for cathodically coloring electrochromic electrodes in electrochromic devices.

Our measured dielectric constant and mechanical response of multiferroic BiFeO 3 indicate four phase transitions below room temperature. Features correlate with those reported at 50 K (from a peak in the zero-field-cooled magnetic susceptibility) and 230 K (from splitting between field-cooled and zero-field-cooled magnetic data; Singh et al 2008 Phys. Rev. B 77 144403), and those at 140 and 200 K (from the magnon light scattering cross section; Singh et al 2008 J.

Magnetization ͑M͒ data on a ferromagnetic/antiferromagnetic ͑FM/AF͒ sample made of a permalloy thin film sputtered on a thick NiO single-crystal substrate reveal remarkable irreversibilities. The field, temperature ͑T͒, and time dependencies of M were measured after the sample was cooled in zero-field or in the presence of a field, keeping T below the Néel temperature, with the field applied in the plane, either perpendicular or parallel to the anisotropy direction. While the behavior observed in the perpendicular configuration is characteristic of spin glasses, in the parallel configuration it exhibits features of random-field systems. The observed metastabilities and thermal history dependencies are shown to result from frustrations and randomness due to the interface roughness.

A method is presented that uses grouping to improve local classification of image primitives. The grouping process is based upon a spin-glass system, where the image primitives are treated as possessing a spin. The system is subject to an energy functional consisting of a local and a bilocal part, allowing interaction between the image primitives. Instead of defining the state of lowest energy as the grouping result, the mean state of the system is taken. In this way, instabilities caused by multiple minima in the energy are being avoided. The means of the spins are taken as the a posteriori probabilities for the grouping result. In the paper, it is shown how the energy functional can be learned from example data. The energy functional is defined in such a way that, in case of no interactions between the elements, the means of the spins equal the a priori local probabilities. The grouping process enables the fusion of the a priori local and bilocal probabilities into the a posteriori probabilities. The method is illustrated both on grouping of line elements in synthetic images and on vessel detection in retinal fundus images.

We present a theoretical framework to accurately calculate the location of the multicritical point in the phase diagram of spin glasses. The result shows excellent agreement with numerical estimates. The basic idea is a combination of the duality relation, the replica method, and the gauge symmetry. An additional element of the renormalization group, in particular in the context of hierarchical lattices, leads to impressive improvements of the predictions. * Dedicated to Prof. A. Nihat Berker on the occasion of his sixtieth birthday.

An outstanding open problem is whether collective social phenomena occurring over short timescales can systematically reduce cultural heterogeneity in the long run, and whether offline and online human interactions contribute differently to the process. Theoretical models suggest that short-term collective behavior and longterm cultural diversity are mutually excluding, since they require very different levels of social influence. The latter jointly depends on two factors: the topology of the underlying social network and the overlap between individuals in multidimensional cultural space. However, while the empirical properties of social networks are intensively studied, little is known about the large-scale organization of real societies in cultural space, so that random input specifications are necessarily used in models. Here we use a large dataset to perform a high-dimensional analysis of the scientific beliefs of thousands of Europeans. We find that interopinion correlations determine a nontrivial ultrametric hierarchy of individuals in cultural space. When empirical data are used as inputs in models, ultrametricity has strong and counterintuitive effects. On short timescales, it facilitates a symmetry-breaking phase transition triggering coordinated social behavior. On long timescales, it suppresses cultural convergence by restricting it within disjoint groups. Moreover, ultrametricity implies that these results are surprisingly robust to modifications of the dynamical rules considered. Thus the empirical distribution of individuals in cultural space appears to systematically optimize the coexistence of short-term collective behavior and long-term cultural diversity, which can be realized simultaneously for the same moderate level of mutual influence in a diverse range of online and offline settings.

This note relates the storage capacity of the Hopfield model of neural networks with possibly correlated patterns to a moderate deviation upper bound for the empirical correlation of the patterns. Examples are, among others, independent patterns with spins that are correlated as in an Ising model or as in a Curie-Weiss model. r

The distribution of interaction fields of an Ising-like system, obtained by Monte Carlo entropic sampling is used for modeling the hysteretic behavior of patterned media made of magnetic particles with a common anisotropy axis; a variant of the canonical Edwards-Anderson Ising spin glass model is introduced. r

The identification of transcription factor binding sites (TFBSs) on genomic DNA is of crucial importance for understanding and predicting regulatory elements in gene networks. TFBS motifs are commonly described by Position Weight Matrices (PWMs), in which each DNA base pair contributes independently to the transcription factor (TF) binding. However, this description ignores correlations between nucleotides at different positions, and is generally inaccurate: analysing fly and mouse in vivo ChIPseq data, we show that in most cases the PWM model fails to reproduce the observed statistics of TFBSs. To overcome this issue, we introduce the pairwise interaction model (PIM), a generalization of the PWM model. The model is based on the principle of maximum entropy and explicitly describes pairwise correlations between nucleotides at different positions, while being otherwise as unconstrained as possible. It is mathematically equivalent to considering a TF-DNA binding energy that depends additively on each nucleotide identity at all positions in the TFBS, like the PWM model, but also additively on pairs of nucleotides. We find that the PIM significantly improves over the PWM model, and even provides an optimal description of TFBS statistics within statistical noise. The PIM generalizes previous approaches to interdependent positions: it accounts for co-variation of two or more base pairs, and predicts secondary motifs, while outperforming multiple-motif models consisting of mixtures of PWMs. We analyse the structure of pairwise interactions between nucleotides, and find that they are sparse and dominantly located between consecutive base pairs in the flanking region of TFBS. Nonetheless, interactions between pairs of non-consecutive nucleotides are found to play a significant role in the obtained accurate description of TFBS statistics. The PIM is computationally tractable, and provides a general framework that should be useful for describing and predicting TFBSs beyond PWMs. Citation: Santolini M, Mora T, Hakim V (2014) A General Pairwise Interaction Model Provides an Accurate Description of In Vivo Transcription Factor Binding Sites. PLoS ONE 9(6): e99015.

Abstract. The cluster variation method has been developed into a general theoretical framework for treating short-range correlations in many-body systems after it was first proposed by Kikuchi in 1951. On the numerical side, a message-passing approach called generalized belief propagation (GBP) was proposed by Yedidia, Freeman and Weiss about a decade ago as a way of computing the minimal value of the cluster variational free energy and the marginal distributions of clusters of variables. However the GBP equations are often redundant, and it is quite a non-trivial task to make the GBP iteration converges to a fixed point. These drawbacks hinder the application of the GBP approach to finite-dimensional frustrated and disordered systems.
In this work we report an alternative and simple derivation of the GBP equations starting from the partition function. Based on this derivation we propose a natural and systematic way of removing the redundance of the GBP equations. We apply the simplified generalized belief propagation (SGBP) equations to the two-dimensional and the three-dimensional ferromagnetic Ising model and Edwards-Anderson spin glass model. The numerical results confirm that the SGBP message-passing approach is able to achieve satisfactory performance on these model systems. We also suggest that a subset of the SGBP equations can be neglected in the numerical iteration process without affecting the final results.

The replica-symmetric postulated MAP analysis can be readily applied to many estimators used in compressed sensing, including basis pursuit, lasso, linear estimation with thresholding, and zero norm-regularized estimation. In the case of lasso estimation the scalar estimator reduces to a soft-thresholding operator, and for zero norm-regularized estimation it reduces to a hard-threshold. Among other benefits, the replica method provides a computationally-tractable method for precisely predicting various performance metrics including mean-squared error and sparsity pattern recovery probability.

Unusual positive exchange bias found in Fe/CoOx nanoparticle bilayer films is correlated to a characteristic magnetic spin-glass (SG) in CoOx, with the SG magnetization coupled antiparallel with the Fe magnetization upon field cooling. This SG magnetization has strong field- and time-dependence which displays unusual upward magnetic relaxation behavior in thermoremanent magnetization measurements. The antiparallel coupling is shown to result predominantly from the antiferromagnetic superexchange of the Fe2+-O-Co3+ couple, of the oxygen-terminated CoOx at the interface. These experimental results reveal the possibility of manipulating the exchange bias effect via an indirect exchange coupling mechanism.

An outstanding open problem is whether collective social phenomena occurring over short timescales can systematically reduce cultural heterogeneity in the long run, and whether offline and online human interactions contribute differently to the process. Theoretical models suggest that short-term collective behavior and long-term cultural diversity are mutually excluding, since they require very different levels of social influence. The latter jointly depends on two factors: the topology of the underlying social network and the overlap between individuals in multidimensional cultural space. However, while the empirical properties of social networks are well understood, little is known about the large-scale organization of real societies in cultural space, so that random input specifications are necessarily used in models. Here we use a large dataset to perform a highdimensional analysis of the scientific beliefs of thousands of Europeans. We find that inter-opinion correlations determine a nontrivial ultrametric hierarchy of individuals in cultural space, a result unaccessible to one-dimensional analyses and in striking contrast with random assumptions. When empirical data are used as inputs in models, we find that ultrametricity has strong and counterintuitive effects, especially in the extreme case of long-range online-like interactions bypassing social ties. On short time-scales, it strongly facilitates a symmetry-breaking phase transition triggering coordinated social behavior. On long time-scales, it severely suppresses cultural convergence by restricting it within disjoint groups. We therefore find that, remarkably, the empirical distribution of individuals in cultural space appears to optimize the coexistence of short-term collective behavior and long-term cultural diversity, which can be realized simultaneously for the same moderate level of mutual influence. This also shows that long-range interactions may simultaneously enhance coordination and sustain diversity.

The magnetically ordered states of the YNixMn1−xO3 and EuNixMn1−xO3 solid solutions (0.0≤x≤0.50) have been studied at different temperatures and magnetic fields. The magnetization as a function of temperature M(T) shows features due to canted-antiferromagnetism (x=0.25 and 0.33) and ferromagnetism (x=0.50), while YNi0.20Mn0.80O3 presents a spin-glass behavior. A large field-dependence of the susceptibility maximum at Tmax is found in the nickel-poor

Our measured dielectric constant and mechanical response of multiferroic BiFeO 3 indicate four phase transitions below room temperature. Features correlate with those reported at 50 K (from a peak in the zero-field-cooled magnetic susceptibility) and 230 K (from splitting between field-cooled and zero-field-cooled magnetic data; Singh et al 2008 Phys. Rev. B 77 144403), and those at 140 and 200 K (from the magnon light scattering cross section; Singh et al 2008 J.

We have recently shown that BiFeO 3 has at least four different magnetic phases, contrary to the conventional wisdom. Below room temperature it undergoes spin reorientation transitions at T 2 ¼ 200 K and T 1 ¼ 140 K analogous to those in orthoferrites; and above room temperature it undergoes a structural transition near 1851C first reported by Polomska et al. This may help explain the apparent linear magnetoelectric effect at 201C reported by D. Lebeugle et al. [Phys. Rev. Lett. 100, 227602 (2008)] which is nominally forbidden due to the long wavelength cycloidal spin structure assumed. We also find evidence of an unusual acentric spin glass below ca. 200 K, related not to T N but to T 1 and T 2 .

Ageing in systems without detailed balance is studied in bosonic contact and pair-contact processes with Lévy diffusion. In the ageing regime, the dynamical scaling of the two-time correlation function and two-time response function is found and analysed. Exact results for non-equilibrium exponents and scaling functions are derived. The behaviour of the fluctuationdissipation ratio is analysed. A passage time from the quasi-stationary regime to the ageing regime is defined, in qualitative agreement with kinetic spherical models and p-spin spherical glasses.

We present a general formalism to make the Replica-Symmetric and Replica-Symmetry-Breaking ansatz in the context of Kikuchi's Cluster Variational Method (CVM). Using replicas and the message-passing formulation of CVM we obtain a variational expression of the replicated free energy of a system with quenched disorder, both averaged and on a single sample, and make the hierarchical ansatz using functionals of functions of fields to represent the messages. We obtain a set of integral equations for the message functionals. The main difference with the Bethe case is that the functionals appear in the equations in implicit form and are not positive definite, thus standard iterative population dynamic algorithms cannot be used to determine them. In the simplest cases the solution could be obtained iteratively using Fourier transforms.

We present a mean-field study of the magnetic phase diagram of
Ni1-xMox and
Ni1-xWx alloys. The pair energies that enter
the internal energy part of the free energy are obtained from a
first-principles calculation. We try to understand why spin-glass phase
is not observed in these alloys.

With the aim of describing a general benchmark for several complex systems, we analyze, by means of statistical mechanics, a sparse network with random competitive interactions among dichotomic variables pasted on the nodes. The model is described by an infinite series of order parameters (the multioverlaps) and has two tunable degrees of freedom: the noise level and the connectivity (the averaged number of links). We show that there are no multiple transition lines, one for every order parameter, as a naive approach would suggest, but just one corresponding to ergodicity breaking. We explain this scenario within a novel and simple mathematical technique via a driving mechanism such that, as the first order parameter (the two replica overlap) becomes different from zero due to a real second order phase transition (with properly associated diverging rescaled fluctuations), it enforces all the other multi-overlaps toward positive values thanks to the strong correlations which develop among themselves and the two replica overlap at the critical line.

Measurements were made of in situ X-ray diffraction, electrical resistivity, and magnetic susceptibility for a series of newly found ternary alloys CuMPt 6 with M = Ti, V, Cr, Mn, Fe, Co, and Ni. They possess, after appropriate heat treatment, the Cu 3 Au-type ordered structure, though the ordering is not complete for M = Ni. They are fairly good electrical conductor with a specific resistivity of around 6 × 10 -3 ohm m. A general trend has been found in the magnetic property: nonmagnetic-spin-glass-like-ferromagnetic-paramagnetic, with increasing atomic number of M.

The distribution of interaction fields of an Ising-like system, obtained by Monte Carlo entropic sampling is used for modeling the hysteretic behavior of patterned media made of magnetic particles with a common anisotropy axis; a variant of the canonical Edwards-Anderson Ising spin glass model is introduced. r