nils-herrmann/clean_scirepeval huggingface dataset:
The dielectric boundary force in ion channels: the case of gramicidin

The dielectric boundary force (DBF) is the force that induced charges at dielectric boundaries exert on the charge that induced them. The DBF is present in any electrostatic problem with a non-uniform dielectric constant, and is important in the case of charged particles near dielectric boundaries. Yet, it is absent in common continuum theories of charge distribution and of charge transport, such as Poisson-Boltzmann and Poisson-Nernst-Planck. In this paper we define the DBF, formulate it as a solution of a partial differential equation, and present its crucial importance for ionic permeation through the gramicidin channel. The main permeation characteristics of gramicidin can be explained in terms of a delicate balance between the DBF and the force formed by the permanent charges of the gramicidin polypeptide. This balance, characteristic of a device, might suggest design principles for man-made nanopores.
Saturation of conductance in single ion channels: the blocking effect of the near reaction field.

The ionic current flowing through a protein channel in the membrane of a biological cell depends on the concentration of the permeant ion, as well as on many other variables. As the concentration increases, the rate of arrival of bath ions to the channel's entrance increases, and typically so does the net current. This concentration dependence is part of traditional diffusion and rate models that predict Michaelis-Menten current-concentration relations for a single ion channel. Such models, however, neglect other effects of bath concentrations on the net current. The net current depends not only on the entrance rate of ions into the channel, but also on forces acting on ions inside the channel. These forces, in turn, depend not only on the applied potential and charge distribution of the channel, but also on the long-range Coulombic interactions with the surrounding bath ions. In this paper, we study the effects of bath concentrations on the average force on an ion in a single ion channel. We show that the force of the reaction field on a discrete ion inside a channel embedded in an uncharged lipid membrane contains a blocking (shielding) term that is proportional to the square root of the ionic bath concentration. We then show that different blocking strengths yield different behavior of the current-concentration and conductance-concentration curves. Our theory shows that at low concentrations, when the blocking force is weak, conductance grows linearly with concentration, as in traditional models, e.g., Michaelis-Menten formulations. As the concentration increases to a range of moderate shielding, conductance grows as the square root of concentration, whereas at high concentrations, with high shielding, conductance may actually decrease with increasing concentrations: the conductance-concentration curve can invert. Therefore, electrostatic interactions between bath ions and the single ion inside the channel can explain the different regimes of conductance-concentration relations observed in experiments.
Models of boundary behavior of particles diffusing between two concentrations

Flux between regions of different concentration occurs in nearly every device involving diffusion, whether an electrochemical cell, a bipolar transistor, or a protein channel in a biological membrane. Diffusion theory has calculated that flux since the time of Fick (1855), and the flux has been known to arise from the stochastic behavior of Brownian trajectories since the time of Einstein (1905), yet the mathematical description of the behavior of trajectories corresponding to different types of boundaries is not complete. We consider the trajectories of non-interacting particles diffusing in a finite region connecting two baths of fixed concentrations. Inside the region, the trajectories of diffusing particles are governed by the Langevin equation. At the interface between the region and the baths, trajectories are set by a control mechanism that modifies dynamics so the concentration of particles remains (nearly) constant. We analyze different models of controllers and derive equations for the time evolution and spatial distribution of particles inside the domain. Our analysis shows a distinct difference between the time evolution and the steady state concentrations. While the time evolution of the density is governed by an integral operator, the spatial distribution is governed by the familiar Fokker-Planck operator. The boundary conditions for the time dependent density depend on the model of the controller; however, this dependence disappears in the steady state, if the controller is of a renewal type. Renewal-type controllers, however, produce spurious boundary layers that can be catastrophic in simulations of charged particles, because even a tiny net charge can have global effects. The design of a non-renewal controller that maintains concentrations of non-interacting particles without creating spurious boundary layers at the interface requires the solution of the time-dependent Fokker-Planck equation with absorption of outgoing trajectories and a source of ingoing trajectories on the boundary (the so called albedo problem).
Ionic diffusion through confined geometries: from Langevin equations to partial differential equations

Ionic diffusion through and near small domains is of considerable importance in molecular biophysics in applications such as permeation through protein channels and diffusion near the charged active sites of macromolecules. The motion of the ions in these settings depends on the specific nanoscale geometry and charge distribution in and near the domain, so standard continuum type approaches have obvious limitations. The standard machinery of equilibrium statistical mechanics includes microscopic details, but is also not applicable, because these systems are usually not in equilibrium due to concentration gradients and to the presence of an external applied potential, which drive a non-vanishing stationary current through the system. We present a stochastic molecular model for the diffusive motion of interacting particles in an external field of force and a derivation of effective partial differential equations and their boundary conditions that describe the stationary non-equilibrium system. The interactions can include electrostatic, Lennard-Jones and other pairwise forces. The analysis yields a new type of Poisson–Nernst–Planck equations, that involves conditional and unconditional charge densities and potentials. The conditional charge densities are the non-equilibrium analogues of the well studied pair correlation functions of equilibrium statistical physics. Our proposed theory is an extension of equilibrium statistical mechanics of simple fluids to stationary non-equilibrium problems. The proposed system of equations differs from the standard Poisson–Nernst–Planck system in two important aspects. First, the force term depends on conditional densities and thus on the finite size of ions, and second, it contains the dielectric boundary force on a discrete ion near dielectric interfaces. Recently, various authors have shown that both of these terms are important for diffusion through confined geometries in the context of ion channels.
Dielectric boundary force and its crucial role in gramicidin.

In an electrostatic problem with nonuniform geometry, a charge Q in one region induces surface charges [called dielectric boundary charges (DBC)] at boundaries between different dielectrics. These induced surface charges, in return, exert a force [called dielectric boundary force (DBF)] on the charge Q that induced them. The DBF is often overlooked. It is not present in standard continuum theories of (point) ions in or near membranes and proteins, such as Gouy-Chapman, Debye-Huckel, Poisson-Boltzmann or Poisson-Nernst- Planck. The DBF is important when a charge Q is near dielectric interfaces, for example, when ions permeate through protein channels embedded in biological membranes. In this paper, we define the DBF and calculate it explicitly for a planar dielectric wall and for a tunnel geometry resembling the ionic channel gramicidin. In general, we formulate the DBF in a form useful for continuum theories, namely, as a solution of a partial differential equation with boundary conditions. The DBF plays a crucial role in the permeation of ions through the gramicidin channel. A positive ion in the channel produces a DBF of opposite sign to that of the fixed charge force (FCF) produced by the permanent charge of the gramicidin polypeptide, and so the net force on the positive ion is reduced. A negative ion creates a DBF of the same sign as the FCF and so the net (repulsive) force on the negative ion is increased. Thus, a positive ion can permeate the channel, while a negative ion is excluded from it. In gramicidin, it is this balance between the FCF and DBF that allows only singly charged positive ions to move into and through the channel. The DBF is not directly responsible, however, for selectivity between the alkali metal ions (e.g., Li+, Na+, K+): we prove that the DBF on a mobile spherical ion is independent of the ion's radius.
Connecting a Discrete Ionic Simulation to a Continuum

An important problem in simulating ions in solution is the connection ofthe finite simulation region to the surrounding continuum bath. In this paper we consider this connection for a simulation ofuncharged independent Brownian particles and discuss the relevance ofthe results to a simulation ofcharged particles (ions). We consider a simulation region surrounded by a buffer embedded in a continuum bath. We analyze the time course ofthe exchange process ofparticles between the simulation region and the continuum, including re-entrances ofparticles that lef t the simulation. We partition the particle population into (i) those that have not yet visited the simulation and (ii) those that have. While the arrival process into the simulation ofpopulation (i) is Poissonian with known rate, that ofpopulation (ii) is more complex. We identif y the ordered set ofre-entrance times ofpopulation (ii) as a superposition ofan infinite number ofdelayed terminating renewal processes, where the renewal periods may be infinite with positive probability. The ordered entrance times ofpopulations (i) and (ii) f orm the pooled process ofinjection times ofparticles into the simulation. We show that while the pooled process is stationary, it is not Poissonian but rather has infinite memory. Yet, under some conditions on the sizes ofthe simulation and buffer regions, it can be approximated by a Poisson process. This seems to be the first result on the time course ofa discrete simulation ofa test volume embedded in a continuum.
A PDE Formulation of Non‐Equilibrium Statistical Mechanics for Ionic Permeation

When there is a steady net flux in a system of interacting particles, the microscopic structure of the system can no longer be determined from the Boltzmann equilibrium distribution (partition function). Nonetheless, the microscopic structure of a finite system of diffusing interacting particles can be described by Poisson‐Nernst‐Planck‐type partial differential equations. These equations, defined in a finite domain, are the non‐equilibrium generalization of the BBGKY hierarchy of equilibrium statistical mechanics. Indeed, when no‐flux conditions are imposed on the domain boundaries, equilibrium results are recovered. When non‐homogeneous boundary conditions are given for these equations, the solutions describe densities and electrostatic potentials of particle systems not in equilibrium. The construction of a pair correlation function under these conditions will be a new result in statistical physics. As in the equilibrium case, a closure relation between a higher and a lower order correlation function h...
The Stationary Arrival Process of Independent Diffusers from a Continuum to an Absorbing Boundary Is Poissonian

We consider the arrival process of infinitely many identical independent diffusion processes from an infinite bath to an absorbing boundary. Previous results on this problem were confined to independent Brownian particles arriving at an absorbing sphere. The present paper extends these results to general diffusion processes, without any symmetries and without resorting to explicit expressions for solutions to the relevant equations. It is shown that for general absorbing boundaries and force fields, the steady stream of arrivals is Poissonian with rate equal to the total flux on the absorbing boundary, as calculated from the continuum theory of diffusion with transport. The considered arrival problem arises in the theory of Langevin simulations of ions in electrolytic solutions. In a Langevin simulation ions enter and exit the simulation region, and it is necessary to compute the probability laws for their entrance times into the simulation. While the simulated ions inside the small simulation region inte...
Derivation of Poisson and Nernst-Planck equations in a bath and channel from a molecular model.

Permeation of ions from one electrolytic solution to another, through a protein channel, is a biological process of considerable importance. Permeation occurs on a time scale of micro- to milliseconds, far longer than the femtosecond time scales of atomic motion. Direct simulations of atomic dynamics are not yet possible for such long-time scales; thus, averaging is unavoidable. The question is what and how to average. In this paper, we average a Langevin model of ionic motion in a bulk solution and protein channel. The main result is a coupled system of averaged Poisson and Nernst-Planck equations (CPNP) involving conditional and unconditional charge densities and conditional potentials. The resulting NP equations contain the averaged force on a single ion, which is the sum of two components. The first component is the gradient of a conditional electric potential that is the solution of Poisson's equation with conditional and permanent charge densities and boundary conditions of the applied voltage. The second component is the self-induced force on an ion due to surface charges induced only by that ion at dielectric interfaces. The ion induces surface polarization charge that exerts a significant force on the ion itself, not present in earlier PNP equations. The proposed CPNP system is not complete, however, because the electric potential satisfies Poisson's equation with conditional charge densities, conditioned on the location of an ion, while the NP equations contain unconditional densities. The conditional densities are closely related to the well-studied pair-correlation functions of equilibrium statistical mechanics. We examine a specific closure relation, which on the one hand replaces the conditional charge densities by the unconditional ones in the Poisson equation, and on the other hand replaces the self-induced force in the NP equation by an effective self-induced force. This effective self-induced force is nearly zero in the baths but is approximately equal to the self-induced force in and near the channel. The charge densities in the NP equations are interpreted as time averages over long times of the motion of a quasiparticle that diffuses with the same diffusion coefficient as that of a real ion, but is driven by the averaged force. In this way, continuum equations with averaged charge densities and mean-fields can be used to describe permeation through a protein channel.
Randomized Approximation Schemes for Cuts and Flows in Capacitated Graphs

We describe random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time randomized combinatorial construction that transforms any graph on $n$ vertices into an $O(n\log n)$-edge graph on the same vertices whose cuts have approximately the same value as the original graph's. In this new graph, for example, we can run the $\tilde{O}(m^{3/2})$-time maximum flow algorithm of Goldberg and Rao to find an $s$-$t$ minimum cut in $\tilde{O}(n^{3/2})$ time. This corresponds to a $(1+\epsilon)$-times minimum $s$-$t$ cut in the original graph. A related approach leads to a randomized divide-and-conquer algorithm producing an approximately maximum flow in $\tilde{O}(m\sqrt{n})$ time. Our algorithm can also be used to improve the running time of sparsest cut approximation algorithms from $\tilde{O}(mn)$ to $\tilde{O}(n^2)$ and to accelerate several other recent cut and flow algorithms. Our algorithms are based on a general theorem analyzing the concent...
On approximating the longest path in a graph

AbstractWe consider the problem of approximating the longest path in undirected graphs. In an attempt to pin down the best achievable performance ratio of an approximation algorithm for this problem, we present both positive and negative results. First, a simple greedy algorithm is shown to find long paths in dense graphs. We then consider the problem of finding paths in graphs that are guaranteed to have extremely long paths. We devise an algorithm that finds paths of a logarithmic length in Hamiltonian graphs. This algorithm works for a much larger class of graphs (weakly Hamiltonian), where the result is the best possible. Since the hard case appears to be that of sparse graphs, we also consider sparse random graphs. Here we show that a relatively long path can be obtained, thereby partially answering an open problem of Broderet al.
 To explain the difficulty of obtaining better approximations, we also prove hardness results. We show that, for any ε<1, the problem of finding a path of lengthn-nε in ann-vertex Hamiltonian graph isNP-hard. We then show that no polynomial-time algorithm can find a constant factor approximation to the longest-path problem unlessP=NP. We conjecture that the result can be strengthened to say that, for some constant δ>0, finding an approximation of rationδ is alsoNP-hard. As evidence toward this conjecture, we show that if any polynomial-time algorithm can approximate the longest path to a ratio of
$$2^{O(\log ^{1 - \varepsilon } n)} $$
, for any ε>0, thenNP has a quasi-polynomial deterministic time simulation. The hardness results apply even to the special case where the input consists of bounded degree graphs.
Fresnel: A Browser-Independent Presentation Vocabulary for RDF

Semantic Web browsers and other tools aimed at displaying RDF data to end users are all concerned with the same problem: presenting content primarily intended for machine consumption in a human-readable way. Their solutions differ but in the end address the same two high-level issues, no matter the underlying representation paradigm: specifying (i) what information contained in RDF models should be presented (content selection) and (ii) how this information should be presented (content formatting and styling). However, each tool currently relies on its own ad hoc mechanisms and vocabulary for specifying RDF presentation knowledge, making it difficult to share and reuse such knowledge across applications. Recognizing the general need for presenting RDF content to users and wanting to promote the exchange of presentation knowledge, we designed Fresnel as a browser-independent vocabulary of core RDF display concepts. In this paper we describe Fresnel’s main concepts and present several RDF browsers and visualization tools that have adopted the vocabulary so far.
Relo: Helping Users Manage Context during Interactive Exploratory Visualization of Large Codebases

As software systems grow in size and use more third-party libraries and frameworks, the need for developers to understand unfamiliar large codebases is rapidly increasing. In this paper, we present a tool, Relo, which supports developers' understanding by allowing interactive exploration of code. As the developer explores relationships found in the code, Relo builds and automatically manages the context in visualization, thereby helping build the developer's mental representation of the code. Developers can group viewed artifacts or use the viewed items to ask Relo for further exploration suggestions, with Relo providing features to limit the growth of the diagram. To ensure developers don't get overwhelmed, Relo has been built with a user-centered approach, and preliminary evaluations with developers exploring new code have shown them to find the tool intuitive and helpful
Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.
First-price path auctions

We study first-price auction mechanisms for auctioning flow between given nodes in a graph. A first-price auction is any auction in which links on winning paths are paid their bid amount; the designer has flexibility in specifying remaining details. We assume edges are independent agents with fixed capacities and costs, and their objective is to maximize their profit. We characterize all strong ε-Nash equilibria of a first-price auction, and show that the total payment is never significantly more than, and often less than, the well known dominant strategy Vickrey-Clark-Groves mechanism. We then present a randomized version of the first-price auction for which the equilibrium condition can be relaxed to ε-Nash equilibrium. We next consider a model in which the amount of demand is uncertain, but its probability distribution is known. For this model, we show that a simple ex ante first-price auction may not have any ε-Nash equilibria. We then present a modified mechanism with 2-parameter bids which does have an ε-Nash equilibrium. For a randomized version of this 2-parameter mechanism we characterize the set of all eNEs and prove a bound on the total payment in any eNE.
End-user application development for the semantic web

Although a lot of information has become readily accessible and necessary for daily work, the current infrastructure for managing information is ill-suited for information-oriented activities: information and functionality are scattered across applications and websites, making it difficult to aggregate and reuse just the right set of content and operations required for unique user tasks. We discuss a collection of tools built into the Haystack platform that address many of the shortcomings of current applications, and allow composing reusable fragments of information and associated operations and views from the Semantic Web into a task workspace tailored to the user and the task. Users can change the workspace to immediately meet changing requirements to easily include, remove or reuse information in multiple tasks simultaneously. The time that a user invests for the initial setup and occasional updates to the workspace is amortized over the numerous times he or she returns to the task, and all relevant information resources are co-located and ready to use.