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While theophylline has been extensively studied with multiple polymorphs discovered, there is still currently no conclusive structure for the metastable theophylline form III. In this present work, by combining more widely used techniques such as X-ray diffraction and thermogravimetric analysis with more emerging techniques like low-frequency Raman and terahertz time-domain spectroscopy, to analyze the structure and dynamics of a crystalline system, it was possible to provide further evidence that the form III structure has a theophylline monohydrate structure with the water molecules removed. Solid-state density functional theory simulations were paramount in proving that this proposed structure is correct and explain how vibrational modes within the crystal structures feature and govern polymorphic transitions and the metastable form III. Through the insight provided by both simulated and experimental results, it was possible to decisively conclude the elusive crystal structure of theophylline form III. It was also shown that the correct space group for theophylline monohydrate is not P21/n but, in fact, Pc.

The ability to identify biomarkers of psychosis risk is essential in defining effective preventive measures to potentially circumvent the transition to psychosis. Using samples of people at clinical high risk for psychosis (CHR) and Healthy controls (HC) who were administered a task fMRI paradigm, we used a framework for labelling time windows of fMRI scans as ‘integrated’ FC networks to provide a granular representation of functional connectivity (FC). Periods of integration were defined using the ‘cartographic profile’ of time windows and k‐means clustering, and sub‐network discovery was carried out using Network Based Statistics (NBS). There were no network differences between CHR and HC groups. Within the CHR group, using integrated FC networks, we identified a sub‐network negatively associated with longitudinal changes in the severity of psychotic symptoms. This sub‐network comprised brain areas implicated in bottom‐up sensory processing and in integration with motor control, suggesting it may be related to the demands of the fMRI task. These data suggest that extracting integrated FC networks may be useful in the investigation of biomarkers of psychosis risk., A framework for extracting epochs of integrated functional connectivity was used to test network differences between healthy control and clinical high‐risk (CHR) groups, as well as associations with longitudinal changes in symptom and functioning scores in CHR participants. A sub‐network suggestive of bottom‐up sensory processing was found to be associated with changes in positive psychotic symptoms in the CHR group. We suggest this to be a useful approach in searching for network‐based biomarkers of psychosis risk.

In the present study, we aim at investigating whether education modulates dynamical properties of time-varying whole-brain network connectivity (the chronnectome) in frontotemporal dementia (FTD) at a given level of symptom severity. Dynamic connectivity parameters were evaluated in 128 patients with FTD using independent component analysis, sliding-time window correlation, and k-means approach to resting state-magnetic resonance imaging data. We evaluated the relationship between education, a proxy measure of cognitive reserve, and 4 indexes of metastate dynamic connectivity: (1) the number of distinct metastates a patient passes through, (2) the number of switches from one metastate to another, (3) the span of the realized metastates, and (4) the total distance traveled in the state space. We found a significant inverse correlation between years of education and the 4 indexes of metastate dynamic fluidity (all p-values ≤ 0.03, false discovery rate-corrected). This study suggests that patients with FTD with higher education but comparable clinical severity show more global functional brain impairment, suggesting that patients with higher cognitive reserve can cope with more global brain fluidity reduction.

The extracellular microenvironment proved to exert a potent regulatory effect over different aspects of Embryonic Stem Cells (ESCs) behavior. In particular, the employment of engineered culture surfaces aimed at modulating ESC self-organization resulted effective in directing ESCs toward specific fate decision. ESCs fluctuate among different levels of functional potency and in this context the Zscan4 gene marks the so-called "metastate," a cellular state in which ESCs retain both self-renewal and pluripotency capabilities. Here we investigated the impact of topographic cues on ESCs pluripotency, differentiation and organization capabilities. To this aim, we engineered culturing platforms of nanograted surfaces with different features size and we investigated their impact on ESCs multicellular organization and Zscan4 gene expression. We showed that the morphology of ESC-derived aggregates and Zscan4 expression are strictly intertwined. Our data suggest that ESC Zscan4 metastate can be promoted if the adhesive surface conditions guide cellular self-aggregation into 3D dome-like structure, in which both cell-material interactions and cell-cell contact are supportive for Zscan4 expression.

We consider the energy difference restricted to a finite volume for certain pairs of incongruent ground states (if they exist) in the d-dimensional Edwards-Anderson (EA) Ising spin glass at zero temperature. We prove that the variance of this quantity with respect to the couplings grows at least proportionally to the volume in any dimension greater than or equal to two. An essential aspect of our result is the use of the excitation metastate. As an illustration of potential applications, we use this result to restrict the possible structure of spin glass ground states in two dimensions., Comment: 9 pages. arXiv admin note: text overlap with arXiv:1403.1208

We investigate the question of whether chaotic size dependence occurs on hierarchical lattices and demonstrate that it is not present in these systems. Our results show that the metastate for spin glasses on hierarchical lattices is simple.

The spontaneous dynamic characteristics of resting-state functional networks contain much internal brain physiological or pathological information. The metastate analysis of brain functional networks is an effective technique to quantify the essence of brain functional connectome dynamics. However, the widely used functional connectivity-based metastate analysis ignored the topological structure, which could be locally reflected by node centrality. In this study, 23 healthy young volunteers (21–26 years) were recruited and scanned twice with a 1-week interval. Based on the time sequences of node centrality, we promoted a node centrality-based clustering method to find metastates of functional connectome and conducted a test-retest experiment to assess the stability of those identified metastates using the described method. The hub regions of metastates were further compared with the structural networks’ organization to depict its potential relationship with brain structure. Results of extracted metastates showed repeatable dynamic features between repeated scans and high overlapping rate of hub regions with brain intrinsic sub-networks. These identified hub patterns from metastates further highly overlapped with the structural hub regions. These findings indicated that the proposed node centrality-based metastates detection method could reveal reliable and meaningful metastates of spontaneous dynamics and indicate the underlying nature of brain dynamics as well as the potential relationship between these dynamics and the organization of the brain connectome.

We study ground states of Ising models with random ferromagnetic couplings, proving the triviality of all zero-temperature metastates. This result sheds a new light on the properties of these systems, putting strong restrictions on their possible ground state structure. Open problems related to existence of interface-supporting ground states are stated and an interpretation of the main result in terms of first-passage and random surface models in a random environment is presented.

The concept of metastate measures on the states of a random spin system was introduced to be able to treat the large-volume asymptotics for complex quenched random systems, like spin glasses, which may exhibit chaotic volume dependence in the strong-coupling regime. We consider the general issue of the extremal decomposition for Gibbsian specifications which depend measurably on a parameter that may describe a whole random environment in the infinite volume. Given a random Gibbs measure, as a measurable map from the environment space, we prove measurability of its decomposition measure on pure states at fixed environment, with respect to the environment. As a general corollary we obtain that, for any metastate, there is an associated decomposition metastate, which is supported on the extremes for almost all environments, and which has the same barycenter., Comment: 12 pages

Significance We address the important question of the temporal organization of large-scale brain networks, finding that the spontaneous transitions between networks of interacting brain areas are predictable. More specifically, the network activity is highly organized into a hierarchy of two distinct metastates, such that transitions are more probable within, than between, metastates. One of these metastates represents higher order cognition, and the other represents the sensorimotor systems. Furthermore, the time spent in each metastate is subject-specific, is heritable, and relates to behavior. Although evidence of non–random-state transitions has been found at the microscale, this finding at the whole-brain level, together with its relation to behavior, has wide implications regarding the cognitive role of large-scale resting-state networks., The brain recruits neuronal populations in a temporally coordinated manner in task and at rest. However, the extent to which large-scale networks exhibit their own organized temporal dynamics is unclear. We use an approach designed to find repeating network patterns in whole-brain resting fMRI data, where networks are defined as graphs of interacting brain areas. We find that the transitions between networks are nonrandom, with certain networks more likely to occur after others. Further, this nonrandom sequencing is itself hierarchically organized, revealing two distinct sets of networks, or metastates, that the brain has a tendency to cycle within. One metastate is associated with sensory and motor regions, and the other involves areas related to higher order cognition. Moreover, we find that the proportion of time that a subject spends in each brain network and metastate is a consistent subject-specific measure, is heritable, and shows a significant relationship with cognitive traits.

We consider the one-dimensional model of a spin glass with independent Gaussian-distributed random interactions, that have mean zero and variance $1/|i-j|^{2\sigma}$, between the spins at sites $i$ and $j$ for all $i\neq j$. It is known that, for $\sigma>1$, there is no phase transition at any non-zero temperature in this model. We prove rigorously that, for $\sigma>3/2$, any Newman-Stein metastate for the ground states (i.e.\ the frequencies with which distinct ground states are observed in finite size samples in the limit of infinite size, for given disorder) is trivial and unique. In other words, for given disorder and asymptotically at large sizes, the same ground state, or its global spin flip, is obtained (almost) always. The proof consists of two parts: one is a theorem (based on one by Newman and Stein for short-range two-dimensional models), valid for all $\sigma>1$, that establishes triviality under a convergence hypothesis on something similar to the energies of domain walls, and the other (based on older results for the one-dimensional model) establishes that the hypothesis is true for $\sigma>3/2$. In addition, we derive heuristic scaling arguments and rigorous exponent inequalities which tend to support the validity of the hypothesis under broader conditions. The constructions of various metastates are extended to all values $\sigma>1/2$. Triviality of the metastate in bond-diluted power-law models for $\sigma>1$ is proved directly., Comment: 18 pages. v2: subsection on bond-diluted models added, few extra references. 19 pages. v3: published version; a few changes; 20 pages

Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d=3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a "dispersed" metastate, supported on many thermodynamic states., Comment: 5 pages, 5 figures

We consider a general class of disordered mean-field models where both the spin variables and disorder variables take finitely many values. To investigate the size-dependence in the phase-transition regime we construct the metastate describing the probabilities to find a large system close to a particular convex combination of the pure infinite-volume states. We show that, under a non-degeneracy assumption, only pure states are seen, with non-random probability weights for which we derive explicit expressions in terms of interactions and distributions of the disorder variables. We provide a geometric construction distinguishing invisible states (having zero weights) from visible ones. As a further consequence we show that, in the case where precisely two pure states are available, these must necessarily occur with the same weight, even if the model has no obvious symmetry relating the two., Comment: 30 pages, 2 figures

Pluripotency confers Embryonic Stem Cells (ESCs) the ability to differentiate in ectoderm, endoderm, and mesoderm derivatives, producing the majority of cell types. Although the majority of ESCs divide without losing pluripotency, it has become evident that ESCs culture consists of multiple cell populations with different degrees of potency that are spontaneously induced in regular ESC culture conditions. Zscan4, a key pluripotency factor, marks ESC subpopulation that is referred to as high-level of pluripotency metastate. Here, we report that in ESC cultures treated with retinoic acid (RA), Zscan4 ESCs metastate is strongly enhanced. In particular, we found that induction of Zscan4 metastate is mediated via RA receptors (RAR-alpha, RAR-beta, and RAR-gamma), and it is dependent on phosphoinositide-3-kinase (PI3K) signaling. Remarkably, Zscan4 metastate induced by RA lacks canonical pluripotency genes Oct3/4 and Nanog but retained both self-renewal and pluripotency capabilities. Finally we demonstrated that the conditional ablation of Zscan4 subpopulation is dispensable for both endoderm and mesoderm but is required for ectoderm lineage. In conclusion, our research provides new insights about the role of RA signaling during ESCs high pluripotency metastate fluctuation.

We present results of numerical simulations on a one-dimensional Ising spin glass with long-range interactions. Parameters of the model are chosen such that it is a proxy for a short-range spin glass above the upper critical dimension (i.e. in the mean-field regime). The system is quenched to a temperature well below the transition temperature $T_c$ and the growth of correlations is observed. The spatial decay of the correlations at distances less than the dynamic correlation length $\xi(t)$ agrees quantitatively with the predictions of a static theory, the "metastate", evaluated according to the replica symmetry breaking (RSB) theory. We also compute the dynamic exponent $z(T)$ defined by $\xi(t) \propto t^{1/z(T)}$ and find that it is compatible with the mean-field value of the critical dynamical exponent for short range spin glasses., Comment: 5 pages, 3 figures

Many scholars have advocated that the cornerstone of sound environmental management is an effective control of stability of the human life-support system. A common theme running through these suggestions is that we should maximize the inherent stability of the life-support system. This essay proposes a new scheme or technique of classifying the stability of systems. Then the essay describes how the stabilizing mechanisms may be considered as a force that holds the human life-support system intact. Stabilizing energy is the energy available to do work, without compromising the integrity of the configuration. The anthropogenic processes of harvesting or using the system as a sink for pollutants are the counterforce that tends to destabilize the system. The basic conclusion is that if society is using a system, then the maximum energy of the anthropogenic processes cannot exceed the stabilizing energy. If this occurs, the system reaches its metastate. Copyright © 2005 John Wiley & Sons, Ltd and ERP Environment.

We investigate numerically the time dependence of "window" overlaps in a three-dimensional Ising spin glass below its transition temperature after a rapid quench. Using an efficient GPU implementation, we are able to study large systems up to lateral length $L=128$ and up to long times of $t=10^8$ sweeps. We find that the data scales according to the ratio of the window size $W$ to the non-equilibrium coherence length $\xi(t)$. We also show a substantial change in behavior if the system is run for long enough that it globally equilibrates, i.e. $\xi(t) \approx L/2$, where $L$ is the lattice size. This indicates that the local behavior of a spin glass depends on the spin configurations (and presumably also the bonds) far away. We compare with similar simulations for the Ising ferromagnet. Based on these results, we speculate on a connection between the non-equilibrium dynamics discussed here and averages computed theoretically using the "metastate"., Comment: 9 pages, 8 figures

We prove the impossibility of recent attempts to decouple the Replica Symmetry Breaking (RSB) picture for finite-dimensional spin glasses from the existence of many thermodynamic (i.e., infinite-volume) pure states while preserving another signature RSB feature—space filling relative domain walls between different finite-volume states. Thus revisions of the notion of pure states cannot shield the RSB picture from the internal contradictions that rule out its physical correctness in finite dimensions at low temperature in large finite volume.

Parisi's formal replica-symmetry--breaking (RSB) scheme for mean-field spin glasses has long been interpreted in terms of many pure states organized ultrametrically. However, the early version of this interpretation, as applied to the short-range Edwards-Anderson model, runs into problems because as shown by Newman and Stein (NS) it does not allow for chaotic size dependence, and predicts non-self-averaging that cannot occur. NS proposed the concept of the metastate (a probability distribution over infinite-size Gibbs states in a given sample that captures the effects of chaotic size dependence) and a non-standard interpretation of the RSB results in which the metastate is non-trivial and is responsible for what was called non-self-averaging. Here we use the effective field theory of RSB, in conjunction with the rigorous definitions of pure states and the metastate in infinite-size systems, to show that the non-standard picture follows directly from the RSB mean-field theory. In addition, the metastate-averaged state possesses power-law correlations throughout the low temperature phase; the corresponding exponent $\zeta$ takes the value $4$ according to the field theory in high dimensions $d$, and describes the effective fractal dimension of clusters of spins. Further, the logarithm of the number of pure states in the decomposition of the metastate-averaged state that can be distinguished if only correlations in a window of size $W$ can be observed is of order $W^{d-\zeta}$. These results extend the non-standard picture quantitatively; we show that arguments against this scenario are inconclusive., Comment: 32 pages. v2: various small changes and additional references. v3: yet more small changes; published version

For pt.II. see ibid., vol.46, p.1916-29 (1998). Hidden Markov models (HMMs) have been used to model single channel currents as recorded with the patch clamp technique from living cells. Continuous time patch-clamp recordings are typically passed through an antialiasing filter and sampled before analysis. In this paper, an adaptation of the Baum-Welch weighted least squares (BW-WLS) algorithm called the H-noise algorithm is presented to estimate the HMM and noise model parameters from bandlimited, sampled data. The effects of the antialiasing filter and the correlated background noise are considered in a metastate or vector HMM framework. The "correlated emission probability", which plays a central role in the algorithm, is redefined to consider the noise correlation in successive filtered, sampled data points. The performance of the H-noise algorithm is demonstrated with simulated data.

We study a ``two-pattern'' Hopfield model with Gaussian disorder. We find that there are infinitely many pure states at low temperatures in this model, and we find that the metastate is supported on an infinity of symmetric pairs of pure states. The origin of this phenomenon is the random breaking of a rotation symmetry of the distribution of the disorder

We investigate the size dependence of disordered spin models having an infinite number of Gibbs measures in the framework of a simplified 'random energy model for size dependence'. We introduce two versions (involving either independent random walks or branching processes), that can be seen as generalizations of Derrida's random energy model. Our model is shown to exhibit a recurrence/transience transition for Gibbs measures (meaning: a.s. existence/nonexistence of subsequences of volumes converging to a given random infinite volume state), depending on the growthrate of a function MN describing the 'number of extremal Gibbs states that can be observed in a finite volume N'. We investigate the model in detail in the 'critical regime' M-N similar to (logN)(p) (With critical point p = 1). We obtain the a.s. large volume asymptotics of the relative weights for finding a particular state and we compute the set of a.s. cluster points of the corresponding occupation times (corresponding to the 'empirical metastate'). In the course of the proof we obtain Laws of the Iterated Logarithm for the pair X-N(v), Y-N(v) : sup(mu = 1,2,...,MN;mu not equal v) X-N(mu) where (X-N(mu)) (mu = 1,...,MN;N = 1,2,....) is either a branching random walk or a collection of random walks, independent over mu.

Embryonic Stem cells (ESCs) can be differentiated into ectoderm, endoderm, and mesoderm derivatives, producing the majority of cell types. In regular culture conditions, ESCs' self-renewal is maintained through molecules that inhibit spontaneous differentiation enabling long-term cellular expansion. This undifferentiating condition is characterized by multiple metastable states that fluctuate between self-renewal and differentiation balance. Here, we aim to characterize the high-pluripotent ESC metastate marked by the expression of Zscan4 through a supervised machine learning framework based on an ensemble of support vector machine (SVM) classifiers. Our study revealed a leukaemia inhibitor factor (Lif) dependent not-canonical pluripotency signature (AF067063, BC061212, Dub1, Eif1a, Gm12794, Gm13871, Gm4340, Gm4850, Tcstv1/3, and Zfp352), that specifically marks Zscan4 ESCs' fluctuation. This novel ESC metastate is enhanced by highpluripotency culture conditions obtained through Extracellular signal Regulated-Kinase (ERK) and Glycogen synthase kinase- 3 (Gsk-3) signaling inhibition (2i). Significantly, we reported that the conditional ablation of the novel ESC metastate marked by the expression of Gm12794 is required for ESCs self-renewal maintenance. In conclusion, we extend the comprehension of ESCs biology through the identification of a novel molecular signature associated to pluripotency programming. Copyright: © 2014 Cerulo et al.

We provide rigorous proofs which show that the main features of the Parisi solution of the Sherrington-Kirkpatrick spin glass are not valid for more realistic spin glass models in any dimension and at any temperature., LaTeX file, 8 pages

We extend the construction by Kuelske and Iacobelli of metastates in finite-state mean-field models in independent disorder to situations where the local disorder terms are are a sample of an external ergodic Markov chain in equilibrium. We show that for non-degenerate Markov chains, the structure of the theorems is analogous to the case of i.i.d. variables when the limiting weights in the metastate are expressed with the aid of a CLT for the occupation time measure of the chain. As a new phenomenon we also show in a Potts example that, for a degenerate non-reversible chain this CLT approximation is not enough and the metastate can have less symmetry than the symmetry of the interaction and a Gaussian approximation of disorder fluctuations would suggest., Comment: 20 pages, 2 figures

Properties of Random Overlap Structures (ROSt)'s constructed from the Edwards-Anderson (EA) Spin Glass model on $\Z^d$ with periodic boundary conditions are studied. ROSt's are $\N\times\N$ random matrices whose entries are the overlaps of spin configurations sampled from the Gibbs measure. Since the ROSt construction is the same for mean-field models (like the Sherrington-Kirkpatrick model) as for short-range ones (like the EA model), the setup is a good common ground to study the effect of dimensionality on the properties of the Gibbs measure. In this spirit, it is shown, using translation invariance, that the ROSt of the EA model possesses a local stability that is stronger than stochastic stability, a property known to hold at almost all temperatures in many spin glass models with Gaussian couplings. This fact is used to prove stochastic stability for the EA spin glass at all temperatures and for a wide range of coupling distributions. On the way, a theorem of Newman and Stein about the pure state decomposition of the EA model is recovered and extended., Comment: 27 pages

In the context of short-range Edwards-Anderson spin glasses, we propose an approach to obtaining rigorous results based on combining the use of metastates, translation-ergodicity and the dependence of certain quantities on small changes of one or more couplings (or fields). This seems especially suited to showing that the structure of thermodynamic states cannot be too complex. As an illustration, we use this approach to prove that thermodynamic states appearing in (e.g.) the periodic boundary condition metastate cannot decompose into a number of pure state pairs strictly between one and infinity.

This paper presents the specifications and the design of a simple graphical interface for building hierarchical finite state machines. This kind of tool can prove very useful for quickly designing hierarchical behaviors. It can be used in the frame of RoboCup to develop deterministic complex behaviors without focusing on C++ coding because source code can be generated from the interface. It is also possible to use it to generate hierarchical finite state machines for whatever purpose needed. The user can create state diagrams by drawing boxes for states and specifying transitions between states. A state diagram can represent a behavior and be considered as a metastate. Diagrams of metastates are possible to constitute several levels.

We discuss the metastate, a probability measure on thermodynamic states, and its usefulness in addressing difficult questions pertaining to the statistical mechanics of systems with quenched disorder, in particular short-range spin glasses. The possible low-temperature structures of realistic (i.e., short-range) spin glass models are described, and a number of fundamental open questions are presented.

In this topical review we discuss the nature of the low-temperature phase in both infinite-ranged and short-ranged spin glasses. We analyze the meaning of pure states in spin glasses, and distinguish between physical, or ``observable'', states and (probably) unphysical, ``invisible'' states. We review replica symmetry breaking, and describe what it would mean in short-ranged spin glasses. We introduce the notion of thermodynamic chaos, which leads to the metastate construct. We apply these tools to short-ranged spin glasses, and conclude that replica symmetry breaking, in any form, cannot describe the low-temperature spin glass phase in any finite dimension. We then discuss the remaining possible scenarios that_could_ describe the low-temperature phase, and the differences they exhibit in some of their physical properties -- in particular, the interfaces that separate them. We also present rigorous results on metastable states and discuss their connection to thermodynamic states. Finally, we discuss some of the differences between the statistical mechanics of homogeneous systems and those with quenched disorder and frustration., Comment: 66 pages (LaTeX); 8 figures; submitted to Journal of Physics: Condensed Matter; Summary and Discussion section added (new Section 10)

The command generator tracker (CGT) approach to model reference adaptive control of linear time-invariant multi-input, multi-output plants is considered. An algorithm is presented for controllable and observable non-ASPR (almost strictly positive real) plants. This algorithm is characterized by the presence of supplementary dynamics in a feedback path inside the adaptive mechanism. These additional dynamics process the output error to form a signal which is multiplied by a new adaptive gain. Therefore, the algorithm differs from other CGT adaptive control algorithms for non-ASPR plants, which require supplementary dynamics to be inserted in parallel with the plant. A generalized metastate representation of the closed-loop adaptive system is proposed. This representation is utilized together with Lyapunov's second method to prove the boundedness of the true error between the plant and model outputs in the presence of bounded plant input and output disturbances. >

We study a Gaussian Potts-Hopfield model. Whereas for Ising spins and two disorder variables per site the chaotic pair scenario is realized, we find that for q-state Potts spins [{q(q-1} \over 2]-tuples occur. Beyond the breaking of a continous stochastic symmetry, we study the fluctuations and obtain the Newman-Stein metastate description for our model., Comment: latex, 17 pages