Renormalization Group-Motivated Learning

We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space RG in a lattice while considers the overall information loss in momentum-space RG. Here we compromise the two measures for the non-spatial data set. For weakly correlated data close to Gaussian, we use the correlation of data as a metric for the proximity of data points, but minimize an overall projection error for optimal coarse-graining steps. It compresses the data to maximize the correlation between the two data points to be compressed while minimizing the correlation between the paired data and other data points. We show that this approach can effectively reduce the dimensionality of the data while preserving the essential features. We extend our method to incorporate non-linear features by replacing correlation measures with mutual information. This results in an information-bottleneck-like trade-off: maximally compress the data while preserving the information among the compressed data and the rest. Indeed, our approach can be interpreted as an exact form of information-bottleneck-like trade off near linear data. We examine our method with random Gaussian data and the Ising model to demonstrate its validity and apply glass systems. Our approach has potential applications in various fields, including machine learning and statistical physics

Electric Double Layer from Phase Demixing Reinforced by Strong Coupling Electrostatics

Ionic liquids (ILs) are appealing electrolytes for their favorable physicochemical properties. However, despite their longstanding use, understanding the capacitive behavior of ILs remains challenging. This is largely due to the formation of a non-conventional electric double layer (EDL) at the electrode-electrolyte interface. This study shows that the short-range Yukawa interactions, representing the large anisotropically charged ILs, demix IL to create a spontaneous surface charge separation, which is reinforced by the strongly coupled charge interaction. The properties of the condensed layer, the onset of charge separation, and the rise of overscreening and crowding critically depend on the asymmetry of Yukawa interactions

Financial Market Crash and Phase Transition: Through Model-Free Framework with Machine Learning

Recent studies have attempted to understand market crash using the concept of phase transition in statistical physics. This study finds certain behavior in the financial market such as the critical phenomena that occur during phase transition. We apply model-free framework using convolutional neural network methods instead of the complex mathematical models studied previously. The results show that the financial market crash has a similar behavior to the phase transition of particles. Furthermore, we find that the similar behavior between financial market crash and phase transition gives better understanding on the market crash and detecting it

Molecular Hydration Tunes the Cation–π Interaction Strength in Aqueous Solution

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Local Dynamics of Excitations in Glassy Liquids

In this study, we propose new elementary processes of the excitation dynamics in glassy liquids, which trigger the structural rearrangement in a local and isolated region known as the cooperative rearrangement region. We identify the existence of primary particles which facilitate local dynamics by using a machine learning technique and a time series analysis. The local soft domains are established by a few soft particles that hop between local energy basins. While particles in contact with these primary soft particles respond non-linearly, other particles not in direct contact with them respond linearly as elastic materials

Two Local States of Ambient Water

The non-monotonic trends of thermodynamic response functions have long been a mystery of water. The idea, that water may be a mixture of two local states, came out more than a century ago to explain the origin of the non-monotonic behaviors. Recently, this idea is materialized through the hypothesis of the second critical point of water and then the anomalies are outcomes of critical fluctuation. Although the typical macroscopic heterogeneity (Widom line) of critical fluctuation stays in the vicinity of the critical point, as we have previously shown that the microscopic heterogeneity is identified far from it which extends the linear heterogeneity, the Widom line, to the areal one as a Widom Delta. With this background, we search for two local states of the ambient water. Distinct states in ambient condition are not to be contrasted by a single strong feature such as density but they are expressed by a combination of weak features that reflects locally correlated structures. In this work, we identify the formation of local bicontinuous micro-domain formations of water attributing its softness by using machine learning order parameters. Interestingly, the radial distribution functions are similar to two phases in the liquid-liquid phase transition and they are well fitted by the two-state model. The hard-label domain is dominant at a lower temperature but changes its label to a more fluctuating soft-label domain at high temperature. There exist crossover behaviors around 310-320 K. At sufficiently high temperatures, near the liquid-gas phase transition, all water molecules become homogeneous

Charge Renormalization for Ellipsoidal Macroions

We study the problem of counterion condensation for ellipsoidal macroions, a geometry well-suited for modeling liquid crystals, anisotropic vesicles, and polymers. We find that the ions within an ellipsoid’s condensation layer are relatively unrestricted in their motions, and consequently work to establish a quasi-equipotential at its surface. This simplifies the application of Alexander et al.’s procedure, enabling us to obtain accurate analytic estimates for the critical valence of a general ellipsoid in the weak screening limit. Interestingly, we find that the critical valence of an eccentric ellipsoid is always larger than that of the sphere of equal volume, implying that counterion condensation provides a force resisting the deformation of spherical macroions. This contrasts with a recent study of flexible spherical macroions, which observed a preference for deformation into flattened shapes when considering only linear effects. Our work suggests that the balance of these competing forces might alter the nature of the transition

Molecular and structural basis of low interfacial energy of complex coacervates in water

Complex coacervate refers to a phase-separated fluid, typically of two oppositely charged polyelectrolytes in solution, representing a complex fluid system that has been shown to be of essential interest to biological systems, as well as for soft materials processing owing to the expectation of superior underwater coating or adhesion properties. The significance and interest in complex coacervate fluids critically rely on its low interfacial tension with respect to water that, in turn, facilitates the wetting of macromolecular or material surfaces under aqueous conditions, provided there is attractive interaction between the polyelectrolyte constituents and the surface. However, the molecular and structural bases of these properties remain unclear. Recent studies propose that the formation of water filled and bifluidic sponge-like nanostructured network, driven by the tuning of electrostatic interactions between the polyelectrolyte constituents or their complexes may be a common feature of complex coacervate fluids that display low fluid viscosity and low interfacial tension, but more studies are needed to verify the generality of these observations. In this review, we summarize representative studies of interfacial tension and ultrastructures of complex coacervate fluids. We highlight that a consensus property of the complex coacervate fluid is the observation of high or even bulk-like water dynamics within the dense complex coacervate phase that is consistent with a low cohesive energy fluid. Our own studies on this subject are enabled by the application of magnetic resonance relaxometry methods relying on spin labels tethered to polyelectrolyte constituents or added as spin labeled probe molecules that partition into the dense versus the equilibrium coacervate phase, permitting the extraction of information on local polymer dynamics, polymer packing and local water dynamics. We conclude with a snapshot of our current perspective on the molecular and structural bases of the low interfacial tension of complex coacervate fluids. (C) 2016 Elsevier B.V. All rights reserved.1194sciescopu