Entropic Cost Research Articles

SAR Signal Formation and Image Reconstruction of a Moving Sea Target

Maritime application of synthetic aperture radar (SAR) technology for sea-target surveillance and imaging is considered in this study. A SAR scenario, including the kinematics of a SAR satellite and a ship moving on the sea, along with the geometry of the target, are analytically described. A linear frequency modulation (LFM) waveform is applied for the target’s illumination. Based on the target’s geometry, SAR and target kinematics and the LFM waveform, a SAR signal model is synthesized. It is proven that the process of signal formation is a transformation of the three-dimensional (3D) image into a two-dimensional (2D) signal, whereas the target’s 2D imaging is an inverse transformation of the 2D signal into the target’s 2D image. SAR signal components, linear Fourier terms and higher-order phase terms are analytically derived and discussed in detail. Moreover, it is proven that SAR image reconstruction is a motion-compensation procedure, i.e., it removes all phases induced by first- and higher-order motion. Based on the SAR signal analysis, an illustrative iterative image-reconstruction algorithm is derived. The quality of the imaging is evaluated by an entropy cost function. Simulation experiments are carried out to verify the correctness of the theoretical statements in respect of SAR signal formation and image reconstruction.

Conformational Entropy as a Potential Liability of Computationally Designed Antibodies.

In silico antibody discovery is emerging as a viable alternative to traditional in vivo and in vitro approaches. Many challenges, however, remain open to enabling the properties of designed antibodies to match those produced by the immune system. A major question concerns the structural features of computer-designed complementarity determining regions (CDRs), including the role of conformational entropy in determining the stability and binding affinity of the designed antibodies. To address this problem, we used enhanced-sampling molecular dynamics simulations to compare the free energy landscapes of single-domain antibodies (sdAbs) designed using structure-based (DesAb-HSA-D3) and sequence-based approaches (DesAbO), with that of a nanobody derived from llama immunization (Nb10). Our results indicate that the CDR3 of DesAbO is more conformationally heterogeneous than those of both DesAb-HSA-D3 and Nb10, and the CDR3 of DesAb-HSA-D3 is slightly more dynamic than that of Nb10, which is the original scaffold used for the design of DesAb-HSA-D3. These differences underline the challenges in the rational design of antibodies by revealing the presence of conformational substates likely to have different binding properties and to generate a high entropic cost upon binding.

Allostery in the dynamic coactivator domain KIX occurs through minor conformational micro-states.

The coactivator KIX of CBP uses two binding surfaces to recognize multiple activators and exhibits allostery in ternary complex formation. Activator•coactivator interactions are central to transcriptional regulation, yet the microscopic origins of allostery in dynamic proteins like KIX are largely unknown. Here, we investigate the molecular recognition and allosteric manifestations involved in two KIX ternary systems c-Myb•KIX•MLL and pKID•KIX•MLL. Exploring the hypothesis that binary complex formation prepays an entropic cost for positive cooperativity, we utilize molecular dynamics simulations, side chain methyl order parameters, and differential scanning fluorimetry (DSF) to explore conformational entropy changes in KIX. The protein’s configurational micro-states from structural clustering highlight the utility of protein plasticity in molecular recognition and allostery. We find that apo KIX occupies a wide distribution of lowly-populated configurational states. Each binding partner has its own suite of KIX states that it selects, building a model of molecular recognition fingerprints. Allostery is maximized with MLL pre-binding, which corresponds to the observation of a significant reduction in KIX micro-states observed when MLL binds. With all binding partners, the changes in KIX conformational entropy arise predominantly from changes in the most flexible loop. Likewise, we find that a small molecule and mutations allosterically inhibit/enhance activator binding by tuning loop dynamics, suggesting that loop-targeting chemical probes could be developed to alter KIX•activator interactions. Experimentally capturing KIX stabilization is challenging, particularly because of the disordered nature of particular activators. However, DSF melting curves allow for inference of relative entropic changes that occur across complexes, which we compare to our computed entropy changes using simulation methyl order parameters.

Absence and recovery of cost-precision tradeoff relations in quantum transport

The operation of many classical and quantum systems in nonequilibrium steady state is constrained by cost-precision (dissipation-fluctuation) tradeoff relations, delineated by the thermodynamic uncertainty relation (TUR). However, coherent quantum electronic nanojunctions can escape such a constraint, showing finite charge current and nonzero entropic cost with vanishing current fluctuations. Here we analyze the absence, and restoration, of cost-precision tradeoff relations in fermionic nanojunctions under different affinities: voltage and temperature biases. With analytic work and simulations, we show that both charge and energy currents can display the absence of cost-precision tradeoffs if we engineer the transmission probability as a boxcar function---with a perfect transmission and hard energy cutoffs. Specifically for charge current under voltage bias, the standard TUR may be immediately violated as we depart from equilibrium, and it is exponentially suppressed with increased voltage. However, beyond idealized, hard-cutoff energy-filtered transmission functions, we show that realistic models with soft cutoffs or imperfect transmission functions follow cost-precision tradeoffs and eventually recover the standard TUR sufficiently far from equilibrium. The existence of cost-precision tradeoff relations is thus suggested as a generic feature of realistic nonequilibrium quantum transport junctions.

Fixed-Point Analysis and FPGA Implementation of Deep Neural Network Based Equalizers for High-Speed PON

Adeep neural network based equalizer is proposed to mitigate the intersymbol interference observed in next generation high speed passive optical network (PON) links. The DNN based equalizer is shown to outperform the best known conventional equalizer, the maximum likelihood sequence estimator (MLSE) both in back-back and through fiber experiments. To reduce the hardware complexity of DNN based equalizer for PON systems, we investigate the use of embedded parallelization within a DNN structure having multiple symbol outputs from one DNN. We further investigate using a classification output stage with cross entropy cost to perform joint decision on multiple symbol outputs and demonstrated that the sensitivity gain of such scheme over regression output. To understand the complexity of hardware implementation, the fixed-point DNN based equalizers are developed and implemented in FPGA. The impact of fixed-point resolution on the receiver sensitivity and hardware resource utilization in FPGA implementation is analyzed and reported in detail. We show that a reduction of over 40% in LUTs (look up table) utilization is possible by reducing the DNN's weight resolution from 8-bit to 4-bit while incurring a small penalty in receiver sensitivity.

How Temperature Rise Can Induce Phase Separation in Aqueous Biphasic Solutions

Ionic-liquid-based acidic aqueous biphasic solutions (AcABSs) recently offered a breakthrough in the field of metal recycling. The particular mixture of tributyltetradecylphosphonium chloride ([P4,4,4,14]Cl), acid, and water presents the unusual characteristic of a lower solution critical temperature (LCST), leading to phase separation upon a temperature rise of typically a few tens of degrees. We address here the microscopic mechanisms driving the phase separation. Using small-angle neutron scattering, we characterized the spherical micelle formation in a binary ionic liquid/water solution and the micelle aggregation upon the addition of acid due to the screening of electrostatic repulsion. The increase in both the acid concentration and the temperature eventually leads to micelle flocculation and phase separation. This last step is achieved through chloride ion adsorption at the surface of the micelle. This exothermic adsorption compensates for the entropic cost, leading to a counterintuitive behavior, and may be generalized to a number of molecular systems with an LCST.

Long-time Behaviour of Entropic Interpolations

In this article we investigate entropic interpolations. These measure valued curves describe the optimal solutions of the Schrödinger problem Schrödinger (Sitzungsberichte Preuss Akad. Wiss. Berlin. Phys. Math. 144:144–153 1931), which is the problem of finding the most likely evolution of a system of independent Brownian particles conditionally to observations. It is well known that in the short time limit entropic interpolations converge to the McCann-geodesics of optimal transport. Here we focus on the long-time behaviour, proving in particular asymptotic results for the entropic cost and establishing the convergence of entropic interpolations towards the heat equation, which is the gradient flow of the entropy according to the Otto calculus interpretation. Explicit rates are also given assuming the Bakry-Émery curvature-dimension condition. In this respect, one of the main novelties of our work is that we are able to control the long time behavior of entropic interpolations assuming the CD(0,n) condition only.

Multi-sensor measurement fusion based on minimum mixture error entropy with non-Gaussian measurement noise

In this paper, a novel multi-sensor measurement fusion method is proposed based on minimum error entropy criterion for nonlinear state estimation in non-Gaussian measurement noise. Through cubature-quadrature transform, a mixture error entropy cost function is defined to capture the high order statistics of multi-source measurement error. Based on the centralized measurement model, a measurement fusion information filter is developed by minimizing the mixture error entropy cost. The fixed point iteration approach is employed to calculate the estimates, and the square root implementation of the proposed filter is also provided. Further, the convergence conditions of the proposed information filter are derived. Simulations are performed with different dimensional measurements to demonstrate the effectiveness of the proposed algorithm. It is shown that, the estimation performance of the proposed measurement fusion information filter is better than that of traditional Kalman and Huber's filter based fusion methods against outliers and Gaussian mixture noises.

Optimal sensor placement for parameter estimation and virtual sensing of strains on an offshore wind turbine considering sensor installation cost

This paper proposes an optimal sensor placement (OSP) framework for parameter estimation, virtual sensing, and condition monitoring using information theory. The framework uses a Bayesian OSP method combined with modal expansion to minimize the information entropy about quantities of interest (QoI), such as strain time histories at critical locations of the structure, without the knowledge of input excitation. The proposed optimization framework also accounts for variations in sensor installation cost at different locations on the monitored structure. The framework is evaluated numerically using a realistic model of an offshore wind turbine on a jacket support structure under installation cost assumptions and considering information entropy of the QoI. The QoI in this numerical study are considered to be the strain time history at one or more locations on the support structure in one problem and the parameters of the structure in the other. A correlation length is considered to account for the spatial correlation of data between adjacent sensors. Effects of the correlation length and input loads on the OSP results for parameter estimation are studied. The considered structural parameters for estimation in this study include (1) modulus of elasticity of tower elements (tower stiffness), (2) modulus of elasticity of jacket elements (jacket stiffness), and (3) vertical foundation spring (soil stiffness). The effect of a subjective weight between the information entropy and sensor configuration cost on the OSP results is also investigated. Different optimal designs are achieved for different weight factors, and the Pareto solutions for OSP are presented. It is found that the OSP framework is an effective tool for decision-makers considering the cost of instrumentation. The presented Pareto optimal solutions can give insight into the value of OSP given a limited budget.

Entropic turnpike estimates for the kinetic Schrödinger problem

We investigate the kinetic Schrödinger problem, obtained considering Langevin dynamics instead of Brownian motion in Schrödinger’s thought experiment. Under a quasilinearity assumption we establish exponential entropic turnpike estimates for the corresponding Schrödinger bridges and exponentially fast convergence of the entropic cost to the sum of the marginal entropies in the long-time regime, which provides as a corollary an entropic Talagrand inequality. In order to do so, we benefit from recent advances in the understanding of classical Schrödinger bridges and adaptations of Bakry–Émery formalism to the kinetic setting. Our quantitative results are complemented by basic structural results such as dual representation of the entropic cost and the existence of Schrödinger potentials.

One-dimensional polymers in random environments: stretching vs. folding

In this article we study a non-directed polymer model on Z, that is a one-dimensional simple random walk placed in a random environment. More precisely, the law of the random walk is modified by the exponential of the sum of potentials βωx−h sitting on the range of the random walk, where (ωx)x∈Z are i.i.d. random variables (the disorder) and β≥0 (disorder strength) and h∈R (external field) are two parameters. When β=0,h>0, this corresponds to a random walk penalized by its range; when β>0,h=0, this corresponds to the “standard” polymer model in random environment, except that it is non-directed. In this work, we allow the parameters β,h to vary according to the length of the random walk and we study in detail the competition between the stretching effect of the disorder, the folding effect of the external field (if h≥0) and the entropy cost of atypical trajectories. We prove a complete description of the (rich) phase diagram and we identify scaling limits of the model in the different phases. In particular, in the case β>0,h=0 of the non-directed polymer, if ωx has a finite second moment we find a range size fluctuation exponent ξ=2∕3.

Reframing the Protein Folding Problem: Entropy as Organizer.

It has been a long-standing conviction that a protein's native fold is selected from a vast number of conformers by the optimal constellation of enthalpically favorable interactions. In marked contrast, this Perspective introduces a different mechanism, one that emphasizes conformational entropy as the principal organizer in protein folding while proposing that the conventional view is incomplete. This mechanism stems from the realization that hydrogen bond satisfaction is a thermodynamic necessity. In particular, a backbone hydrogen bond may add little to the stability of the native state, but a completely unsatisfied backbone hydrogen bond would be dramatically destabilizing, shifting the U(nfolded) ⇌ N(ative) equilibrium far to the left. If even a single backbone polar group is satisfied by solvent when unfolded but buried and unsatisfied when folded, that energy penalty alone, approximately +5 kcal/mol, would rival almost the entire free energy of protein stabilization, typically between -5 and -15 kcal/mol under physiological conditions. Consequently, upon folding, buried backbone polar groups must form hydrogen bonds, and they do so by assembling scaffolds of α-helices and/or strands of β-sheet, the only conformers in which, with rare exception, hydrogen bond donors and acceptors are exactly balanced. In addition, only a few thousand viable scaffold topologies are possible for a typical protein domain. This thermodynamic imperative winnows the folding population by culling conformers with unsatisfied hydrogen bonds, thereby reducing the entropy cost of folding. Importantly, conformational restrictions imposed by backbone···backbone hydrogen bonding in the scaffold are sequence-independent, enabling mutation─and thus evolution─without sacrificing the structure.

Transport of Molecular Cargo by Interaction with Virus‐Like Particle RNA

AbstractVirus‐like particles (VLPs) derived from Leviviridae virions contain substantial amounts of cellular and plasmid‐derived RNA. This encapsidated polynucleotide serves as a reservoir for the efficient binding of the intercalating dye thiazole orange (TO). Polyethylene glycol (PEG) molecules and oligopeptides of varying length, end‐functionalized with TO, were loaded into VLPs up to approximately 50 % of the mass of the capsid protein (hundreds to thousands of cargo molecules per particle, depending on size). The kinetics of TO–PEG binding included a significant entropic cost for the reptation of long chains through the capsid pores. Cargo molecules were released over periods of 20–120 hours following simple reversible first‐order kinetics in most cases. These observations define a simple general method for the noncovalent packaging, and subsequent release, of functional molecules inside nucleoprotein nanocages in a manner independent of modifications to the capsid protein.

Transport of Molecular Cargo by Interaction with Virus-Like Particle RNA.

Virus-like particles (VLPs) derived from Leviviridae virions contain substantial amounts of cellular and plasmid-derived RNA. This encapsidated polynucleotide serves as a reservoir for the efficient binding of the intercalating dye thiazole orange (TO). Polyethylene glycol (PEG) molecules and oligopeptides of varying length, end-functionalized with TO, were loaded into VLPs up to approximately 50 % of the mass of the capsid protein (hundreds to thousands of cargo molecules per particle, depending on size). The kinetics of TO-PEG binding included a significant entropic cost for the reptation of long chains through the capsid pores. Cargo molecules were released over periods of 20-120 hours following simple reversible first-order kinetics in most cases. These observations define a simple general method for the noncovalent packaging, and subsequent release, of functional molecules inside nucleoprotein nanocages in a manner independent of modifications to the capsid protein.

Estimating Entropy Production from Waiting Time Distributions.

Living systems operate far from thermal equilibrium by converting the chemical potential of ATP into mechanical work to achieve growth, replication, or locomotion. Given time series observations of intra-, inter-, or multicellular processes, a key challenge is to detect nonequilibrium behavior and quantify the rate of free energy consumption. Obtaining reliable bounds on energy consumption and entropy production directly from experimental data remains difficult in practice, as many degrees of freedom typically are hidden to the observer, so that the accessible coarse-grained dynamics may not obviously violate detailed balance. Here, we introduce a novel method for bounding the entropy production of physical and living systems which uses only the waiting time statistics of hidden Markov processes and, hence, can be directly applied to experimental data. By determining a universal limiting curve, we infer entropy production bounds from experimental data for gene regulatory networks, mammalian behavioral dynamics, and numerous other biological processes. Further considering the asymptotic limit of increasingly precise biological timers, we estimate the necessary entropic cost of heartbeat regulation in humans, dogs, and mice.

Tunable Knot Segregation in Copolyelectrolyte Rings Carrying a Neutral Segment.

We use Langevin dynamics simulations to study the knotting properties of copolyelectrolyte rings carrying neutral segments. We show that by solely tuning the relative length of the neutral and charged blocks, one can achieve different combinations of knot contour position and size. Strikingly, the latter is shown to vary nonmonotonically with the length of the neutral segment; at the same time, the knot switches from being pinned at the block's edge to becoming trapped inside it. Model calculations relate both effects to the competition between two adversarial mechanisms: the energy gain of localizing one or more of the knot's essential crossings on the neutral segment and the entropic cost of such localization. Tuning the length of the neutral segment sets the balance between the two mechanisms and hence the number of localized essential crossings, which in turn modulates the knot's size. This general principle ought to be useful in more complex systems, such as multiblock copolyelectrolytes, to achieve a more granular control of topological constraints.

Folding in Place: Design of β-Strap Motifs to Stabilize the Folding of Hairpins with Long Loops.

Despite their pivotal role in defining antibody affinity and protein function, β-hairpins harboring long noncanonical loops remain synthetically challenging because of the large entropic penalty associated with their conformational folding. Little is known about the contribution and impact of stabilizing motifs on the folding of β-hairpins with loops of variable length and plasticity. Here, we report a design of minimalist β-straps (strap = strand + cap) that offset the entropic cost of long-loop folding. The judicious positioning of noncovalent interactions (hydrophobic cluster and salt-bridge) within the novel 8-mer β-strap design RW(V/H)W···WVWE stabilizes hairpins with up to 10-residue loops of varying degrees of plasticity (Tm up to 52 °C; 88 ± 1% folded at 18 °C). This "hyper" thermostable β-strap outperforms the previous gold-standard technology of β-strand-β-cap (16-mer) and provides a foundation for producing new classes of long hairpins as a viable and practical alternative to macrocyclic peptides.

Computational design and experimental substantiation of conformationally constrained peptides from the complex interfaces of transcriptional enhanced associate domains with their cofactors in gastric cancer

Transcriptional enhanced associate domains (Teads) are the downstream effectors of the hippo signaling pathway and have been recognized as attractive druggable targets of gastric cancer. The biological function of Teads is regulated by diverse cofactors. In this study, the intermolecular interactions of Teads with their cognate cofactors were systematically characterized at structural, thermodynamic and dynamic levels. The Teads possess a double-stranded helical hairpin that is surrounded by three independent structural elements β-sheet, α-helix and Ω-loop of cofactor proteins and plays a central role in recognition and association with cofactors. A number of functional peptides were split from the hairpin region at Tead–cofactor complex interfaces, which, however, cannot maintain in native conformation without the support of protein context and would therefore incur a considerable entropy penalty upon competitively rebinding to the interfaces. Here, we further used disulfide and hydrocarbon bridges to cyclize and staple the hairpin and helical peptides, respectively. The chemical modification strategies were demonstrated to effectively constrain peptide conformation into active state and to largely reduce peptide flexibility in free state, thus considerably improving their affinity. Since the cyclization and stapling only minimize the indirect entropy cost but do not influence the direct enthalpy effect upon peptide binding, the designed conformationally constrained peptides can retain in their native selectivity over different cofactors. This is particularly interesting because it means that the cyclized/stapled, affinity-improved peptides can specifically compete with their parent Teads for the cofactor arrays as they share consistent target specificity.

Replenishment Model with Entropic Order Quantity for Deteriorating Items under Inflation

The purpose of the current paper is to determine an optimal order quantity so as to minimize the total cost of the inventory system of a business enterprise. The model is developed for deteriorating items with stock and selling price dependent demand under inflation without permitting shortage. Optimal solution is achieved by cost minimization strategy considering replenishment cost, purchase cost, holding cost and deterioration cost with a special approach to entropy cost for bulk size purchasing units. The effectiveness of the proposed model has been avowed through empirical investigation. Sensitivity analysis has been accomplished to deduce managerial insights. Findings suggest that an increased inflationary effect results in increment in the system total cost. The paper can be extended by allowing shortage. The model can be utilized in the business firms dealing with bulk purchasing units of electric equipments, semiconductor devices, photographic films and many more.

LeukoX: Leukocyte Classification Using Least Entropy Combiner (LEC) for Ensemble Learning

This brief proposes a scheme to detect and classify across four different classes of white blood cells (WBC) based on their morphological features by ensemble learning applied over multiple deep neural networks (DNN). Contrary to the DNN based WBC classification schemes, this method makes use of a novel least entropy combiner (LEC) network that effectively combines the individual classifier decisions in order to minimize the cross entropy cost. In this brief, two pretrained DNNs, namely DenseNet121 and ResNet50 are used along with a custom-designed convolutional neural network (CNN) to individually produce the class confidence scores which are fed to the proposed LEC network for the ensemble learning purpose. A dataset comprising of around 12, 500 images of four different WBC types, namely Eosinophil, Lymphocyte, Monocyte, and Neutrophil are considered for training and testing the proposed network. The proposed model yields superior performance than the individual networks. Our results demonstrate that the proposed model achieves an overall test accuracy of 96.67%, with precision and sensitivity scores of 96.73%, and 96.62% respectively and the Matthews correlation coefficient (MCC) and kappa scores being 0.9334 and 0.9550, respectively. The overall model is termed as LeukoX (X: Extended).