Modified Ising Model Research Articles

The effects of vacancy ordering on diffusion: a statistical study

In this paper we investigate the interconnection between vacancy-ordered phases and vacancy self-diffusion. Here, we investigate three ordered phases on a square lattice with energetics defined by two separate Hamiltonians. In the first case we used a classical antiferromagnetic Ising model Hamiltonian in order to generate a 'checkerboard' type ordered structure. In the second case, we used a modified Ising model with competing influence of second and third nearest-neighbors, which resulted in both 'hatch' and 'labyrinthine' structures, depending on concentration. To understand how vacancy-ordering affects diffusion, we determined the tracer diffusivity using rejection-free kinetic Monte Carlo and compared disordered and ordered structures. Finally, we developed an analytical model describing diffusion in the ordered 'checkerboard' structure and found that it was able to predict apparent activation energies in the ordered and disordered structures. Our results suggest that it is short-range order rather than long-range order that most significantly affects tracer diffusion.

Evidence and Structural Insights into a Ligand-Mediated Phase Transition in the Solvated Ligand Shell of Quantum Dots.

As synthesized, nanocrystal surfaces are typically covered in coordinating organic ligands, and the degree of packing and order of these ligands are ongoing questions in the field of colloidal nanocrystals, particularly in the solution state. Recently, isothermal titration calorimetry coupled with 1H NMR has been used to probe ligand exchanges on colloidal quantum dots, revealing the importance of the composition of the ligand shell on exchange thermodynamics. Previous work has shown that the geometry and length of a ligand's aliphatic chain can influence the thermodynamics of exchange. This has been attributed to interligand interactions, and the use of a modified Ising model simulation to account for these collective effects has been critical in describing these reactions. In this report, we explore the reaction between indium phosphide quantum dots and zinc chloride on a size series of nanocrystals capped with two different lengths of aliphatic, straight-chain carboxylate ligands to investigate the effect that nanocrystal size has on these interligand interactions. We demonstrate that interligand interactions increase as the nanocrystal size increases, changing the thermodynamics of the ligand exchange reaction. Critically, we show that a self-consistent model of these ligand exchanges does not fit the data without the use of a phase transition term in the model and that the strength of this phase transition depends on the nanocrystal size. Combined with solution state X-ray diffraction, these results provide indirect evidence that ligands are ordered on nanocrystals in the solution state.

An Ising Model-Based Annealing Processor With 1024 Fully Connected Spins for Combinatorial Optimization Problems

This brief presents a novel annealing processor (AP) design with 1024 fully-connected spins based on a modified Ising model annealing algorithm for combinatorial optimization problems. By adopting the proposed Turbo code-based interleaved random sequence generator (TCSG) and multi-spin update method, the memory usage is made considerable reduction and multi-spin parallel update is supported. The prototype is implemented using FPGA with the operation frequency of 100 MHz. We tested our design on various G-set problems with an average cut accuracy of 99.19% achieved. The proposed design outperforms the CPU-based method by achieving a max speedup of 1099×.

Nucleons as modified Ising models* *S.M.H and J.X. are supported in part by the National Natural Science Foundation of China (12105247) and the China Postdoctoral Science Foundation (2021M702957). Y.S.L is supported in part by the National Natural Science Foundation of China (12002209)

In this paper, we propose a map that connects nucleons bound in nuclei and Ising spins in the Ising model. This proposal is based on the fact that the description of states of nucleons and Ising spins could share the same type of observables. We present a nuclear model corresponding to an explicit modified Ising model and qualitatively confirm the correctness of this map with a simulation on a two-dimensional square lattice. This map can help us understand the profound connections between different physical systems.

Stability Islands and the Folding Cooperativity of a Seven-Repeat Array from Topoisomerase V.

Cooperativity is a central feature of protein folding, but the thermodynamic and structural origins of cooperativity remain poorly understood. To quantify cooperativity, we measured guanidine-induced unfolding transitions of single helix-hairpin-helix (HhH)2 repeats and tandem pairs from a seven-repeat segment of Methanopyrus kandleri Topoisomerase V (Topo V) to determine intrinsic repeat stability and interfacial free energies between repeats. Most single-repeat constructs are folded and stable; moreover, several pairs have unfolding midpoints that exceed midpoints of the single repeats they comprise, demonstrating favorable coupling between repeats. Analyzing unfolding transitions with a modified Ising model, we find a broad range of intrinsic and interfacial free energies. Surprisingly, the G repeat, which lacks density in the crystal structure of Topo V without DNA, is the most stable repeat in the array. Using nuclear magnetic resonance spectroscopy, we demonstrate that the isolated G repeat adopts a canonical (HhH)2 fold and forms an ordered interface with the F-repeat but not with the H repeat. Using parameters from our paired Ising fit, we built a partition function for the seven-repeat array. The multistate unfolding transition predicted from this partition function is in excellent agreement with the experimental unfolding transition, providing strong justification for the nearest-neighbor model. The seven-repeat partition function predicts a native state in which three independent segments ("stability islands") of interacting repeats are separated by two unstable interfaces. We confirm this segmented architecture by measuring the unfolding transition of an equimolar mixture of these three separate polypeptides. This segmented structural organization may facilitate wrapping around DNA.

Impact of Uniform Facets on the Thermodynamics of Ligand Exchanges on Colloidal Quantum Dots

Nanocrystal surfaces play a critical role in dictating their physical and chemical properties. Colloidal semiconductor nanocrystals, or quantum dots, are generally synthesized with insulating aliphatic ligands, but these ligands can be post-synthetically exchanged with other molecular species for a variety of applications. While previous work has investigated the thermodynamics of ligand exchanges on quasi-spherical quantum dots through sensitive isothermal titration calorimetry and 1H NMR measurements, the influence of well-defined crystal facets on the propensity of these ligand exchanges is yet to be explored using these techniques. We studied the exchange of native cadmium carboxylate ligands for zinc chloride ligands on (111) faceted cadmium selenide tetrahedrons and (100) faceted cadmium selenide cubes. From these measurements, we find the unexpected result that the thermodynamics of this ligand exchange between these facets is nearly identical. Further, a modified Ising model was used to fit both the calorimetric and 1H NMR data to extract thermodynamic parameters for the exchange. These simulations suggest that the observed enthalpic differences can be mostly attributed to varying inter-ligand interactions on the (111) and (100) facets.

A Bayesian modified Ising model for identifying spatially variable genes from spatial transcriptomics data

A recent technology breakthrough in spatial molecular profiling (SMP) has enabled the comprehensive molecular characterizations of single cells while preserving spatial information. It provides new opportunities to delineate how cells from different origins form tissues with distinctive structures and functions. One immediate question in SMP data analysis is to identify genes whose expressions exhibit spatially correlated patterns, called spatially variable (SV) genes. Most current methods to identify SV genes are built upon the geostatistical model with Gaussian process to capture the spatial patterns. However, the Gaussian process models rely on ad hoc kernels that could limit the models' ability to identify complex spatial patterns. In order to overcome this challenge and capture more types of spatial patterns, we introduce a Bayesian approach to identify SV genes via a modified Ising model. The key idea is to use the energy interaction parameter of the Ising model to characterize spatial expression patterns. We use auxiliary variable Markov chain Monte Carlo algorithms to sample from the posterior distribution with an intractable normalizing constant in the model. Simulation studies using both simulated and synthetic data showed that the energy-based modeling approach led to higher accuracy in detecting SV genes than those kernel-based methods. When applied to two real spatial transcriptomics (ST) datasets, the proposed method discovered novel spatial patterns that shed light on the biological mechanisms. In summary, the proposed method presents a new perspective for analyzing ST data.

Thermodynamics of Composition Dependent Ligand Exchange on the Surfaces of Colloidal Indium Phosphide Quantum Dots

Quantum dot surfaces can have a substantial effect on their physical, chemical, and optoelectronic properties. When the chemistry that occurs at the surface of nanocrystals is studied, critical insights can be gained into the fundamental structural, thermodynamic, and optical properties of quantum dot materials providing a valuable guide for how to best adapt them for desired applications. Colloidal quantum dots are often terminated with organic ligands that consist of a long aliphatic chain and a head group that binds tightly to the nanocrystal surface. While extensive work has been done to understand how ligand head groups influence quantum dot properties, studies to unravel the influence of the organic ligand tail on ligands and surface reaction equilibria are incomplete. To further investigate the driving forces of quantum dot surface modification, a series of ligand exchange reactions with oleic acid were performed on indium phosphide quantum dots, initially terminated with straight-chain carboxylates of variable lengths. The reaction was monitored using isothermal titration calorimetry and 1H NMR to determine the extent of each reaction and its associated thermodynamics. From these measurements, interligand interactions were observed to be dependent on the length of the straight-chain ligand. A modified Ising model was used to investigate the enthalpic and entropic effects contributing to these ligand exchanges and reveal that interligand interactions play a much larger role than previously thought. Additional experimentation with phosphonic acid ligand exchange reveals complexity in the reaction mechanism but further illustrates the significant impact of ligand tail group length on thermodynamics, even in cases where there is a large difference in head group binding energy.

Diffuse phase transition and thermal hysteresis in relaxor ferroelectrics from modified Ising model

<sec> Relaxor ferroelectric is a very special type of ferroelectric material, which has important applications in communication, sensor, ultrasound, energy conversion, and aerospace industry. Unlike normal ferroelectric, a relaxor undergoes a diffuse phase transition in the cooling process, and its macroscopic polarization does not occur suddenly, but polar nano region appears while the macro-symmetry does not change significantly. As the transition from the paraelecric to the ferroelectric phase is a gradual process with a broad dielectric peak, relaxor ferroelectric has no definite Curie temperature (<i>T</i><sub>C</sub>), and the temperature corresponding to the maximum dielectric constant (<i>T</i><sub>m</sub>) and the Burns temperature (<i>T</i><sub>B</sub>) are often used as their characteristic temperatures.</sec><sec> Here, in order to understand the diffuse phase transition and its internal mechanism, we build a modified Ising model by introducing an energy potential well that affects the spin variable (which is regarded as electric dipole in this research) and simulate the phase transition process using this model, which results in significantly smoothed phase transition with respect to temperature, exhibiting relaxor characteristics with diffuse phase transitions. More precisely, it is found that by applying the energy potential well to the dipoles in the system, the ferroelectric phase transition can be significantly broadened, that is, a diffused phase transition appears, showing strong relaxation characteristics that, as the temperature gradually increases, the average electric dipole moment does not change abruptly while the peak value of its permittivity decreases with the energy potential well. Moreover, at a temperature much higher than the transition temperature of the usual Ising model, the system can still maintain a certain polarization, which is in line with relaxor characteristics. By comparing to a previously proposed statistical model, it is found that the relaxation phenomenon is due to the fact that dipoles in the system are constrained by the given potential well, therefore difficult to flip, making the overall polarizability deviate from that of conventional ferroelectrics. Our results therefore show that the existence of dipole energy potential well is an important factor in the relaxation phenomenon of ferroelectric.</sec><sec> This modified Ising model, which accounts for the constrained dipoles statistically, is then used to investigate the thermal hysteresis effect of relaxor ferroelectrics in order to understand its origin. By comparing to experimental results, we are able to clarify the physics of the thermal hysteresis of relaxor ferroelectric, deepening our understanding from the theoretical and simulation perspective.</sec>

Investigation of domain structure in ferroelectric thin films by means of the Ising model

The domain structure in thin ferroelectric films was investigated in the framework of the modified Ising model with short-range exchange and long-range dipole-dipole interactions. The depolarizing field was also taken into account for the study of size effects in thin films. This field is the dominant factor influencing on the existence of phase transitions in the films. We used Monte Carlo method with the standard Metropolis algorithm to generate configurations on three-dimensional cubic lattices. The domains sizes were calculated in the longitudinal and transverse directions relatively to the spontaneous polarization direction. Temperature dependences of the domain sizes are obtained for different values of interaction constants. It was proved that the introduction of the depolarizing field leads to the appearance of a dead layer on the film boundaries. The dead layer thickness increases with increasing temperature. At a certain temperature (not equal to the Curie temperature), the dead layer is destroyed. The temperature dependences of the dielectric susceptibility at different film thicknesses have been calculated. It was shown that these dependencies have two maxima. The first maximum corresponds to a phase transition, the second one exists only for only thin films and corresponds to the destruction of the dead layer.

A modified Ising model of Barab\xe1si\u2013Albert network with gene-type spins

The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.

One-Dimensional Glassy Behavior of Ultraconfined Water Strings.

Water is renowned for its anomalous behaviors, which can be linked to a distributed H-bond network in bulk water. Ultraconfinement of the water molecule can remove H-bonding, leaving only molecular water. In natural cordierite crystals, water is trapped in an orthorhombic channel with an average diameter of 5.7 Å, running through the center of the unit cell parallel to the c-axis. Calorimetric measurements reveal the existence of a one-dimensional (1D) glass linked to this water. In these channels, water molecules in truncated, sparse 1D strings interact only via dipole-dipole correlations. A physical 1D glass is formed from these strings. This unusual state can be explained by a modified Ising model. This model predicts a dependence of the glass transition temperature, Tg, on the size of these domains. This is confirmed experimentally.

An Expansive Exploration for Novel Liquid Electrolytes through Data-Driven Physics-Based Modeling

Electrolyte development plays a key role in the design of current and future battery chemistries. Almost all of the advanced battery technologies such as lithium metal, high voltage cathodes, dual ion batteries, metal air batteries and other beyond lithium ion battery technologies are bottlenecked by the performance of the electrolytes.[i] ,[ii],[iii] There is an increasing need for electrolytes with large electrochemical windows, wide temperature operating windows, very good ionic conductivity for operation at high rates of charge and discharge, low viscosity, good solubility and low flammability and toxicity from a safety standpoint. Thus, there are a large number of constraints on the electrolytes and they are becoming increasingly stringent. To add to the complexity of electrolyte design, there exist multiple trade-offs between all these properties as shown in previous literature.[iv] Although various solid electrolytes, ionic liquids and polymer electrolytes are being researched, organic liquid electrolytes still outperform the other electrolytes when we consider all the properties required. The current approach of new electrolyte design is largely intuition based using certain structural features in the organic molecules. Currently only a few hundred solvents and salts have been demonstrated in all the battery technologies while there are over 20 million organic molecules discovered. The richness of liquid organic compounds is multiplied even further if we start considering mixtures as most of the properties vary non-linearly as you mix two organic compounds. In this work, we suggest a much better data-driven systematic exploration of new electrolytes. The methodology employs determination of various electronic structure features calculated from simple and scalable density functional theory (DFT) calculations and topological features of the molecules. We will identify unique parameters which are non-linear functions of the above features for each of the properties above along with features that govern mixtures. We currently have structures for over 1 million molecules with over 100,000 data points for each property. This gives a unique capability to identify parameters accurately, explore multiple trade-offs and different methods of overcoming these trade-offs. The cathodic stability of the electrolyte can be described in terms of the highest occupied molecular orbital (HOMO) energy level of each of the components. The HOMO level will be estimated using GGA level DFT, quantitative structure-property relationships (QSPR) and higher order theories and comparisons will be shown. The solubility of a salt is governed by the solvation of the individual ions and the dielectric constant of the solvent as shown by the extended Debye- Hückel and other models. We have developed a modified Ising model to describe solvation shell around the Li+ ions, and the model has been solved under mean field approximations to derive the fraction of all species in the Li+ solvation shell.[v] The model can also be extended to describe other cations and anions and is applicable to mixtures. The Ising model coefficients used for the model are the ion-solvent interactions, ion-ion interactions and solvent-solvent interactions can be calculated from DFT. The dielectric constant, important for solubility is correlated to the dipole moment of molecule. This relationship is quite qualitative as in a liquid, the molecules exist as multiple conformers. To provide more quantitative data, we have identified the volume of molecule calculated using DFT along with number of rotatable bonds as additional geometric features to determine the dielectric constant. The dielectric constant along with the solvation energies will be used to give a feature for solubility. The viscosity of an electrolyte is dependent on the solvation shell structure of ions and the viscosity of the solvent which is related to intermolecular interactions and will be explored. We will also show the relationship between the Li+ solvation energy and charge transfer resistance. We believe this electrolyte exploration method is much more systematic, quantitative, scalable and also able to identify outliers to certain trends. This method and database will create a new frontier for electrolyte discovery for most electrochemical systems and also other areas of science. In the future, we will add features for other physical and chemical properties and also extend these to inorganic compounds.

Design Principles for Electrolytes in Li-O2 Batteries

Among the “beyond Li-ion” battery chemistries, non-aqueous Li-O2 batteries have the highest theoretical specific energy[1] and, as a result, have attracted significant research attention over the past decade. A critical challenge facing non-aqueous Li-O2 batteries is the electronically insulating nature of the primary discharge product, lithium peroxide, which passivates the battery cathode as it is formed, ultimately leading to low ultimate cell capacities. Recently, it has been shown that, to resolve the passivation of cathode, we need to enhance the solubility of the intermediate LiO2 *.[2],[3] This can be done by either solvating the Li+ cation using high donor number (DN) solvents such as (DMSO) or by solvating superoxide anion O2 - using small amount of high acceptor number (AN) solvent additives like water, alcohols. However both these approaches lead to electrolyte formulations that become unstable. High donor number solvents have been shown to be susceptible to nucleophilic attack from superoxide ion (O2 -) formed from the dissolution of LiO2 * intermediate leading to solvent degradation.[4] Water is also known to react with superoxide ion and lithium, increasing the parasitic reactions. This leads to a further decrease in the overall electrochemical stability of the system, thereby deleteriously affecting the rechargeability of the battery. In this study, we report that a significant enhancement (greater than fourfold) in Li-O2 cell capacity is possible by appropriately selecting the salt-solvent combination in the electrolyte solution. A route to decouple this trade-off is to enhance the solvation through appropriate electrolyte salt selection. To quantify the increase in battery capacity for different salt-solvent combinations, we have to develop a theory for determining the Gibbs free energy of Li+ in the electrolyte solution. To a first approximation, the Gibbs free energy of ionic species in solution is primarily dependent on its first solvation shell. In this study, we develop a modified Ising model to derive the solvation shell composition and in turn the Gibbs free energy of Li+. In the Ising model, we describe the possible energetic interactions between all species as functions of the DN and AN of each species that can occupy the solvation shell. Within the mean-field approximation, we derive average occupation for each species in the solvation shell. The average occupation is then used to derive the Li+ Gibbs free energy. We compare the results from the developed model to the 7Li NMR chemical shift and this agrees well for both low DN, DME and high DN solvents, DMSO. From the model, we find that high DN salt anions mixed with low DN solvents give enhanced dissolution of LiO2 * and in turn the cell capacity as compared to high DN solvents. However, high DN salts do not offer additional enhancement of the dissolution rate and capacity when mixed in high DN solvent. However, as pointed out earlier, high DN solvents are unstable and thus, we suggest using low DN solvents with high DN salt anions to give the same increase in capacity without compromising stability. Using this strategy, the challenging task of identifying an electrolyte solvent that possesses anti-correlated properties of high intermediate solubility and solvent stability is alleviated, potentially providing a pathway to develop an electrolyte that affords both high capacity and rechargeability. We will discuss extensions of the model to include interface effects, which become important for cells with thin electrolyte layers. We believe the model and strategy presented here will be generally useful to enhance Coulombic efficiency in many electrochemical systems where improving intermediate stability in solution could induce desired mechanisms of product formation. One limitation of the solubility based increase of cell capacity is the transport of Li+ and O2 - ions in solution will limit the current and thus the power density delivered by the cells. We will present extensions that will explore the trade-off between ion mobility or equivalently current density (or power density) and cell capacity of the Li-O2battery chemistry. [1] Christensen J, Albertus P, Sanchez-Carrera R S, Lohmann T, Kozinsky B, Liedtke R, Ahmed J & Kojic A (2011) A critical review of li/air batteries J. Electrochem. Soc. 159 R1–30 [2] N. B. Aetukuri, et. al. (2015) Solvating additives drive solution-mediated electrochemistry and enhance toroid growth in non-aqueous Li–O2 batteries. Nat. Chem. 7(1), 50-56. [3] Johnson L, et al. (2014) The role of LiO2 solubility in O2 reduction in aprotic solvents and its consequences for Li–O2 batteries. Nature Chem. 6(12):1091-1099. [4] Khetan A, Luntz A, & Viswanathan V (2015) Trade-offs in capacity and rechargeability in nonaqueous Li–O2 batteries: solution-driven growth versus nucleophilic stability. J. Phys. Chem. Lett.:1254-1259 Figure 1

Hysteresis in DNA compaction by Dps is described by an Ising model

In all organisms, DNA molecules are tightly compacted into a dynamic 3D nucleoprotein complex. In bacteria, this compaction is governed by the family of nucleoid-associated proteins (NAPs). Under conditions of stress and starvation, an NAP called Dps (DNA-binding protein from starved cells) becomes highly up-regulated and can massively reorganize the bacterial chromosome. Although static structures of Dps-DNA complexes have been documented, little is known about the dynamics of their assembly. Here, we use fluorescence microscopy and magnetic-tweezers measurements to resolve the process of DNA compaction by Dps. Real-time in vitro studies demonstrated a highly cooperative process of Dps binding characterized by an abrupt collapse of the DNA extension, even under applied tension. Surprisingly, we also discovered a reproducible hysteresis in the process of compaction and decompaction of the Dps-DNA complex. This hysteresis is extremely stable over hour-long timescales despite the rapid binding and dissociation rates of Dps. A modified Ising model is successfully applied to fit these kinetic features. We find that long-lived hysteresis arises naturally as a consequence of protein cooperativity in large complexes and provides a useful mechanism for cells to adopt unique epigenetic states.

Statistical Mechanics of ‘Unwanted Electroactuation’ in Nanoporous Supercapacitors

Nanoporous electrodes have the potential to increase the surface electrode interfacial area and the stored energy density of a supercapacitor. However, structural deformation of the electrode can become apparent when the size of the pore is comparable to the size of a charging ion. After many cycles this could cause wear and degradation. We present a theoretical study of this ‘Unwanted Electroactuation’ in a carbon electrode wetted with an ionic liquid. We incorporate changes of the carbon-carbon bond length due to electrochemical doping of the pore walls and steric effects related to counterion insertion into the pore via a modified Ising model of charge storage. When considering the total electrode deformation these effects either complement or compete with each other, depending on the polarisation of the electrode. Our model shows qualitative agreement with the features of the experimentally observed expansion caused by variation of electrode potential.

Trace membrane additives affect lipid phases with distinct mechanisms: a modified Ising model.

The addition of trace molecules into membranes can significantly alter the morphology of the co-existing liquid phases and lipid phase transition temperature. Membrane additives may affect lipid phase dynamics through preferentially partitioning to the boundary between lipid phases or preferentially mixing into one lipid phase. The characteristic differences between these mechanisms are demonstrated here in a minimalistic nearest neighbor model to provide a framework for how slight changes to membrane composition may affect lipid-phase-dependent processes, such as lipid-raft formation, immunological signaling, and molecular sorting preceding endocytosis with coexisting liquid phases. Within the low mole fractions explored here (≤3 mol%), increasing the additive concentration linearly changed the phase miscibility temperature. Rotationally asymmetric Janus particles reduced the miscibility transition temperature for all fractions and degree of phase polarization. Rotationally symmetric additives, however, either increased or decreased the phase miscibility temperature depending on the phase preference of the additive. While most experimental molecules may contain aspects of both of these idealized additives, this model provides a broad framework to quantify the effects of membrane additives in regard to lipid phase preference, lipid-raft association, and contribution to lipid phase-dependent molecular sorting.Electronic supplementary materialThe online version of this article (doi:10.1007/s00249-015-1017-x) contains supplementary material, which is available to authorized users.

Relative constraints and evolution

Several mathematical models of evolving systems assume that changes in the micro-states are constrained to the search of an optimal value in a local or global objective function. However, the concept of evolution requires a continuous change in the environment and species, making difficult the definition of absolute optimal values in objective functions. In this paper, we define constraints that are not absolute but relative to local micro-states, introducing a rupture in the invariance of the phase space of the system. This conceptual basis is useful to define alternative mathematical models for biological (or in general complex) evolving systems. We illustrate this concept with a modified Ising model, which can be useful to understand and model problems like the somatic evolution of cancer.

The statistics of contour fragments in natural scenes

AbstractSummary: Recent electrophysiology recordings in macaque V4/IT suggest that single neuron response to synthetic closed contours can be largely captured by models which only consider a small number of contour fragments (Brincat and Connor 2004). Motivated by this experimental work, we sought firstly to characterize the statistics of contour fragments in natural scenes, and secondly to generate synthetic images which reflect the measured contour-fragment statistics.To detect contour fragments, we defined a set of feature detectors which respond only in the presence of two edges co-occurring at a fixed relative angle – implemented as a logical ‘AND’ of two Gabor-like, laplacian-of-gaussian linear filters. We then determined the pairwise correlations of these contour fragments in a natural image ensemble. If efficient coding extends to higher cortical centers and processing in the ventral visual stream can be modeled as a sequence of logical operations on linear shape features, then the pairwise statistics we measure should be informative about neural shape coding.Using these statistics directly, it is possible to produce a generative model of simple images which contain the measured statistics. We implemented a modified Ising model and solved the inverse problem of determining the optimal model parameters which satisfy the measured correlations. The resulting Ising-like model of the pairwise statistics can generate the probability of any arrangement of contour fragments as measured in the natural image ensemble.As a complementary approach to producing images with naturalistic contour fragment statistics, it is possible to start with a natural scene and isolate the target features. This is achieved by applying our contour fragment detection processing to the single scene and then separately visualizing the fragments detected. This second procedure lends itself to parametric randomization of the generated image.Narrative Elaboration: The central question guiding our study is how shapes are represented in inferotemporal cortex. To that end, we have investigated natural images in order to motivate experiments capable of targeting the extent to which neural processing of shapes involves representing shapes as combinations of key contour features. To simplify, we are focusing on black-and-white images and prioritizing contour features. This project suggests it is possible to generate synthetic images containing only a select set of contour statistics. Our subsequent goals include conducting collaborative macaque electrophysiology experiments with our generated images as visual stimuli.

Protein Aggregation as a Phase Transition Process

In this model we attempt to mimic the aggregation pattern found in real proteins using a modified Ising model. Similar to a Blume-Campel model, we restrict the proteins to occupy discrete lattice points and define a pairwise interaction depending on the configuration of the protein (as in the Potts model). We define three specific conformational states: native, intermediate and unfolded and consider the aggregation process as a series of second-order phase transitions. In this framework we can analyze the zeros of the partition function analytically continued onto the complex plane, specifically the Yang-Lee and Fisher zeros. Using combinatorial arguments we can simplify the partition function and predict the occurrences of phase transitions as a function of the interaction potential and protein density.