text:
Simulation of diffusion using a modular cell dynamic simulation system
Authors: Leberecht, Christopha; b | Heinke, Floriana; c | Labudde, Dirka; *
Affiliations: [a] Faculty of Applied Computer Sciences and Biosciences, University of Applied Sciences Mittweida, Technikumplatz 17, Mittweida, Germany | [b] Biotechnology Center (BIOTEC), TU Dresden, Tatzberg 47-49, Dresden, Germany | [c] Faculty of Chemistry and Physics, TU Bergakademie Freiberg, Akademiestrasse 6, Freiberg, Germany
Correspondence: [*] Corresponding author: Dirk Labudde, Bldg. 8: Richard-Stuecklen Bau, Office 8-105, Am Schwanenteich 6b, 09648 Mittweida, Germany. Tel.: +49 3727 58 1469; Fax: +49 3727 58 21469; E-mail: dirk.labudde@hs-mittweida.de.
Keywords: Cellular automaton, graph, diffusion, cell biology, systems biology
Journal: In Silico Biology, vol. 12, no. 3-4, pp. 129-142, 2017
Received 19 January 2017
Accepted 13 April 2017
A variety of mathematical models is used to describe and simulate the multitude of natural processes examined in life sciences. In this paper we present a scalable and adjustable foundation for the simulation of natural systems. Based on neighborhood relations in graphs and the complex interactions in cellular automata, the model uses recurrence relations to simulate changes on a mesoscopic scale. This implicit definition allows for the manipulation of every aspect of the model even during simulation. The definition of value rules ω facilitates the accumulation of change during time steps. Those changes may result from different physical, chemical or biological phenomena. Value rules can be combined into modules, which in turn can be used to create baseline models. Exemplarily, a value rule for the diffusion of chemical substances was designed and its applicability is demonstrated. Finally, the stability and accuracy of the solutions is analyzed.
The simulation of complex physical, chemical, and biological phenomena has become an important tool for the research in life sciences. Models that mimic the behavior of natural systems support the understanding and analysis of laboratory experiments [1]. In systems and cell biology such models are valuable for inferring the life-sustaining chemical transformations in cells [2], the self-organization of the cytoskeleton synthesis [3], and phenotypes of whole organisms [4]. Quantitative models are able to give actual predictions about the quantities in a system. Most models are generally systems of ordinary or partial differential equations (PDE). Such systems are composed of multiple equations, where each equation represents the concentration of a chemical compound. It is of high importance to model these equations as accurately as possible to correctly capture the phenomena observed on the biological level. Even small differences in the initial conditions may produce large discrepancies between the simulation and the experimental outcome [5]. Hence, each experimental model has to be addressed differently, and many parameters have to be measured and set to describe the phenomenon observed under specific conditions. While helpful for a small group of scientists, those models can rarely be adapted for problems that are the result of a similar underlying phenomenons [6]. Scientists can only observe consequences of physical and chemical laws that are entangled in complex systems such as cells and organisms. So it is no surprise, that most models do not describe the "real shape" of the problem and only characterize the guise of the phenomenon. For an illustration of the problem, consider a medical doctor who tries to cure an illness. Only by approaching and treating the underlying causes, he can hope to cure the patient. Treating the symptoms is only viable in the most severe cases. Similarly, if we are able to characterize the processes in a cell and know their interactions, it is possible to modify the system and obtain the behavior that is required. The creation of new fundamental laws is a large step in the development of systems biology [7]. Modeling those fundamental processes and combining them as system-theoretic concepts is still one of the greatest challenges in the field of systems biology [8, 9].
One technique to explore the general traits of interacting systems and spatio-temporal patterns are cellular automata (CA). Originated in the 1940s, CA are simulations discrete in time, space, and state. By applying a simple set of rules – which depend on automata elements, so-called cells, and their respective associations between each other – at each time-step, remarkably complex behaviors emerge from such automata [10, 11]. This discrete character to CA is tailored for the computation using traditional computers that operate at finite precision by design. Dynamic Cellular Automata, as an agent-based adaptation of CA, have been shown to describe a multitude of different cellular or biochemical processes [12]. Although CA have been used in many fields of biology [13], they played a minor role in recent years, because powerful tools such as ECell [14] and VCell [15] started to dominate the research field. Both tools and many others alike are based on PDEs that are composed and specified by the user of the software. With all reactions and processes defined, a numerical solution of the system of PDE is generated and calculated. The user is able to inspect the results and adjust parameters to fine-tune the model to fit the results gained via laboratoryexperiments.
Space is one of the key components when modeling the processes in cells. In the last decade simulations in systems biology have been moving from temporal-only models to spatio-temporal models [16]. An established practice for simulations with a spatial component is to partition the simulation space into smaller compartments that are able to exchange components or information. This holds true for CA, which are traditionally defined to handle spatial neighborhood relations on two- or three dimensional geometric tilings. The neighbors of each cell are defined by adjacent edges or corners.
Another approach to model natural systems are stochastic simulation algorithms (SSA) such as Chemical Master Equations (CME), which can be necessary when biological phenomena depend on stochastic fluctuations [17]. CME are able to model diffusion using particle position distributions – which are either compartment-based or reliant on Smoluchowski equations – and chemical reactions, based on probabilities of molecular reactions during a defined time period. Assuming a spatially homogeneous system the changes in concentration can be simulated.
PDEs, SSA and CA represent different techniques to explore the behavior of dynamic systems, all designed to define the change that occurs in events or time steps. In PDEs this change is explicitly defined from the starting point and for all following steps in time. Therefore it is possible to poll the state of the system by solving a single equation. In comparison, using CA, numerical methods, or SSE the next state of the system is implicitly defined by its current state, thus adjusting parameters or even states can be accomplished readily at every time step, but every state in between the current and the required time step has to be calculated [18, 19]. This leads to a consideration of the advantages and disadvantages of implicit definitions in opposition to explicit definitions. The updating procedure of explicit systems depends on the value of the previous time step, and may even be analytically formulated as a closed form solution. Therefore the determination of the updates is straightforward and computationally inexpensive. As a compromise, explicit methods are only conditionally stable, meaning errors at any stage of the computation or divergence in the starting conditions are amplified and not attenuated as the simulation progresses. Hence, explicit solutions require very small time steps, especially when there are major changes in a short time period. Implicit systems can include values of the current and previous time steps. The calculations performed in each time step are generally more difficult, resulting in a higher time complexity of the simulation. Nevertheless, implicit schemes are stable and can tolerate larger time steps than explicitly defined systems [20]. This also includes a robustness to unexpected changes. Especially in biological environments the ability to respond and adjust to spontaneous disturbances, such as molecular signals from other cells or changes in temperature is vital in order to create a realistic and robust model [21].
In 2001 Tomita proposed that systems biology should rise to a grand challenge of the 21st century [22]. The construction of a mathematical model of the whole cell is a key aspect in this challenge. In order to understand the complex system of the cell, the fundamental processes that govern its behavior have to be understood. A modular system that allows to easily add and remove certain aspects of a model is a possible approach to analyze the forces that drive biological systems. A seed model can be used as a basis to experiment with different pathways, reaction types, and parameter sets, without the need to modify the entire system due to adding a single component. To evaluate the possibilities that CA offer for modularized spatio-temporal modeling of natural systems, we define a graph-oriented CA and design a function to simulate diffusion processes. The diffusion of six different molecules within a rectangular shaped space is simulated with the model proposed in this paper and validated with a numerical approach. We discuss the stability of the solutions gained concerning different time and space resolutions and suggest a general guideline to select those parameters. In systems that simulate multiple chemical components and/or multiple phenomena, it can be difficult to select the best size for the time step. In numerical analyses different algorithms are available to estimate a stable step width, such as Ruge-Kutta methods [19]. With the proposed model it is possible to determine the time and spatial step size, without additional estimation methods. The user of the model has the freedom to weigh and choose between simulation accuracy, complexity, and stability before performing the simulation of the system.
2Methods
The concept of cellular graph automata has been pioneered by Angela Wu [23] in the late 1970s. The research with graph automata was mainly focused on investigating the properties of graphs and applications to graph grammars. Nevertheless, the dynamic definition of neighborhood in CA is a powerful aspect to capture geometries that cannot be defined easily by a static geometric definition.
2.1Modeling cellular graph automata
The definition of cellular d-graph automata proposed by Wu and Rosenfeld [23] has been adapted for this work. For reference purposes we will present a short informal definition. A d-graph Γ is a graph with labeled nodes and numbered edges. A distinguished label element # exists – if a node is not labeled with # it has exactly d edges emanating from it. Further a finite-state automaton M on d-graphs is defined as a double (Q, δ), where Q is a nonempty set of states and δ the transition function, which maps a new state to a node depending on the current state, the edge numbers and neighbor states. Further, the cellular d-graph automaton M is a triple (Γ, M, H) with a d-graph Γ and M as defined before and H the neighbor vector of a node n. An automaton M is placed at each node n of Γ. The neighbor vector H supplies the required information about the neighbors.
For the adaption of cellular graph automata (CGA) presented here, we exchanged the definition of d-graphs with finite graphs, that are triplets (X, U, α) where X and U are two finite disjoint sets and α is a function [24]. This implies that nodes and edges are no longer labeled and do not rely on a bounded degree d. Additionally, the states Q is introduced at the level of CGA, because they are globally defined.
Definition 1 (Cellular Graph Automaton). Let a cellular graph automaton be a quadruple CGA = (V, E, Q, α), for which:
· V is a finite set of graph automaton cells,
· E is a finite set,
· Q is a finite set, and
· α : E ↦ V ∪ V is a partial function.
V, E, and Q are disjoint sets. The set V contains the nodes of the graph with elements denoted as v1, v2, …, vn and each element of this set is a graph automaton cell (see Definition 2). Elements e1, e2, …, eu originate from the set of edges E. The set Q = {q1, q2, …, qr} is the set of possible states. The number of elements in each set is given as n = |V|, u = |E|, and r = |Q|. The function α (ei) = (vj, vk) assigns the relation between a pair of nodes vj, vk ∈ V and an edge ei ∈ E. If such a relation exists between two nodes vj, vk they are called neighbors.
A graph automaton cell (GAC) is a modified version of the finite state automaton M, where we keep the essence of the transition function δ.
Definition 2 (Graph automaton cell). Let a graph automaton cell be a triple GAC = (p, δ, q), for which
· p∈ℝg is the position
· δ : Q* ↦ QCGA is a total function (the state rule), and
· q ∈ QCGA is the current state.
The position of a node in a space of dimension g is represented by the position p∈ℝg . Each node is enclosed by the Voronoi region of p, which represents the surface or volume a node is responsible for during the simulation. Formally the Voronoi region Rvk of a node vk can be described by all points in a space x∈ℝg with a metric dR, such that
Rvk={x∈ℝg | dR(x,pvk)≤dR(x,pvj), ∀j≠k},
as described by Aurenhammer in [25]. In the context of CGA the metric dR is called geometric distance.
CGA are composed of nodes, and unlike CA, their neighborhood relations are based upon the connections represented by edges. Let dN be the neighborhood distance of two nodes. In other words: dN defines the number of edges on the shortest path between two nodes. Therefore the distance dN between two nodes vk, vj ∈ V, is dN (vk, vj) =1, if and only if there exists an edge e ∈ E such that α (e) = (vk, vj). Further, the distance dN between two distant nodes v1, vn ∈ V can be defined by the shortest path between them. Hence let (v1, v2, …, vn) ∈ V × V × ⋯ × V be the shortest path between two nodes, such that vi is neighbored to vi+1 for 1 ≤ i < n. The resulting distance will be dN (v1, vn) = n - 1. In contrast to CA, CGA do not define specific boundary conditions. Different pseudo boundaries can be created be adding new edges that specify the desired interactions.
While CA operate in a predefined tiling, GAC act depending on their neighbors, defined by α and represented by a multiset N. Let the multiset N, called neighbor states, be a double N = (Q, m), for which Q is the finite set of states and m:Q↦ℕ is a function. The function m (q) maps a state q ∈ Q to a natural number. This is the number of times a neighboring node is in the state q ∈ Q. If Q ⊂ QCGA, then the multiplicity m of the elements QCGA \ Q is 0. Consequently, the multiset Nvk of a node vk contains the states q of nodes vi that are connected to vk with an edge:
Nvk={qvi∈QCGA|dN(vk,vi)=1}
The cardinality of the multiset is the sum of all multiplicity functions and equal to the degree deg of the node vk:
|Nvk|=∑q∈Qm(q)=deg(vk)
As an example consider a node vk in state q1 with three neighboring nodes in q3 and one neighbor also in state q1. The available states consist of QCGA = {q1, q2, q3}. The resulting multiset of neighbor states is Nvk = {q1, q1, q1, q3} and the appropriate functions are m (q1) =3, m (q2) =0 and m (q3) =1.
The transition of a node from one state q (t) at time t to the next state q (t + Δt) is defined by the state rule δ, which can be either deterministic or stochastic. The step size Δt is uniform. The domain Q* of δ is a multiset of states from QCGA that consists of the neighbor states Nvk, in addition to the state of node vk itself and maps to the next state q (t + Δt) of vk. An exemplary deterministic transition function would be:
δ(Qvk*)={q1ifm(q1)>|N|2,q2ifm(q2)>|N|2,q3else.
This deterministic transition function determines the next state of a node, by the number of neighboring nodes in a certain state. If the number of nodes in state q1 is larger than the number of nodes in state q2 the next state of this node will be q1 and vice versa. The state q3 would be assigned if the number of nodes in q1 and q2 are exactly even.
With these definitions the state of a node can be set. Considering the initial representation of nodes as a segment of space inside of a biological system, possible states could be comprised of the environment or compartment a node is enclosing. In this context, the state of a node may be any organelle, such as chloroplast, endoplasmic reticulum, or Golgi apparatus. The states or objects can be allowed to move through the cell with rules adapted from the String definition in [26] or remain static. In order to handle continuous values, such as concentrations of species, the previous definition is augmented to Extended Graph Automaton Cells (EGAC), which are used to enrich the concept of CGA. Here, each node is able to accommodate a set of entities that represent its content.
The description species is used to generally refer to sets of atoms, molecules, molecular fragments, ions and similar entities, subject to a chemical process or to a measurement. Each species s ∈ S represents such a chemical compound. A value function f(s)∈ℝ maps a value to the species s that represents any quantitative or physicochemical property. The first quantitative property defined for the purpose of this paper is the concentration function fc (s) that maps the concentration of a species s to any node vk. Additionally, the function fd (s) maps a species to its diffusivity. This function is independent from any node, since the diffusivity of a species is considered constant regardless of its position in the CGA. Other functions can readily be implemented, and the set of all value functions is referred to as F .
Definition 3 (Extended graph automaton cell). An extended graph automaton cell is a quintuple EGAC = (δ, Ω, q, W), for which
· δ : Q* ↦ QCGA is a total function (the state rule),
· Ω is a set of functions ω : W* × s ↦ W (the value rules),
· q ∈ QCGA is the current state, and
· W is the current value set.
The Definition 2 of GAC also applies to the multiset Q*, the transition function δ and the current state q. The value functions Ω and the current current value set W are new components to this definition. The value set W contains the sets of values defined by each value function f∈F and for each species s ∈ S. For example, consider two species s1, s2 ∈ S and two value functions fc mapping the concentration and fd mapping the diffusivity of a node vk. The resulting value set could look like Wvk = {{fc (s1) =0.3, fc (s2) =0.4} , {fd (s1) =1.2, fd (s2) =2.7}}.
The domain W* of each value rule ω consists again of the neighboring value sets. Each value set Wvi of the nodes vi that share an edge with the node vk is included in the Mvk set.
Mvk={Wvi|dN(vk,vi)=1}
The set of value rules Ω contains all value rules that are to be applied to the value set of the node vk. A single value rule ω maps from the set of multiple value sets W*, including neighbor value sets Mvk and the node vk itself, to the new value set W. A rule ω is used to calculate the change of any fi (t, v, s) of a species s, at node v and time t. For example, the arithmetic mean of the concentrations in a node can be assigned with:
ωfcAvg(si)=Δfc(vk,si)=1|Wvk*|·∑fc(si)∈Wvk*fc(si).
ωfcAvg(si) denotes the value rule for averaging the concentration fc of any species si, Δfc (vk, si) describes the change in concentration at node vk of the species si and |Wvk*| the number of neighbors of vk. A visualization of this definition and its interpretation is depicted in Fig. 1.
A section of a cellular graph automaton illustrating nodes, edges, and Voronoi regions. A set of species S is globally defined and a set of attributes can be assigned to every individual species. Each extended graph automaton cell (see Definition 3) contains the current concentration fc (si) of a species si. The species and values depicted were only chosen as an example. The value function ωfc (si) defines a rule for the change in concentration for each species.
The idea behind this definition is the creation of multiple value rules that represent natural phenomena inside of the cell. It is possible to define multiple value rules that modify the same value in a value set. For example, consider the diffusion of a species into neighboring compartments in addition to the conversion into another species during a chemical reaction. Both events would modify the concentration of the same species. In this case the sum of the changes for each species and value function will be applied to the node.
The size of the time step is uniform and can be parametrized as described in Section 2.3. This enables the simulation of multiple time scales depending on the phenomenon that is to be addressed. Additionally, the size of the time step provides the possibility to choose between a more accurate prediction (using numerous small time steps) or a faster simulation (using fewer large time steps). A schematic representation of the sequence of operations that are needed to setup and perform a simulation is depicted in Fig. 2.
The flowchart describes the general sequence of steps during the initialization process and actual simulation of CGA.
To evaluate the proposed model, the process of diffusion has been implemented as a value rule ωDif. Diffusion is one of the fundamental processes that governs the behavior of all natural systems on a molecular level. It is possible to derive an implicit value rule that is able to describe the flow of matter between the nodes in CGA. The derivation of this rule is presented in the following section.
2.2Modeling diffusion
Diffusion is a natural physical process in which molecules disperse from an area of high concentration proportional to a concentration gradient. This phenomenon is describes the random motion of all particles in solutions, called Brownian motion. Fick proposed the Second Law of Diffusion, in which the flux of matter in a liquid is proportional to the gradient of its concentration c scaled by a factor D [27]:
∂c∂t=D∂2c∂x2.
This equation needs to be transformed into a recurrence relation, which then enables the implementation into CGA. Using the finite differences method as shown in [20], the infinitesimal small steps in time ∂t and space ∂x can be formulated using finitely small steps Δt and Δx. The concentration was rewritten to c (t, x), to indicate its dependence on time t and the position x:
1Δt(c(t+Δt,x)−c(t,x))︸change of c per Δt=D∂∂x·1Δx(c(t,x+Δx)−c(t,x))︸change of c per Δx.
By calculating the limit with Δx, Δt → 0 of this function, it is possible to reformulate Fick's second law in a discrete manner. The reformulation of the second space-derivative is performed specifically for CGA. Since the introduction of a neighborhood-oriented approach is required, it is necessary to distribute the spatial differences as uniformly as possible around the point of interest x, so that the isotropy of the geometric space is conserved. Subsequently, it is necessary to define the neighborhood of the current position x. Thus, let H = {h1, dotsb, hd} be the set of nodes that are adjacent to a node vk. This relationship is derived by collecting all nodes where dN (vk, hi) =1 (see Definition 1). In conclusion, position x will now be represented as a node vn and hi ∈ H are nodes, that have a distance of Δx = dN to vk. Since there is now a finite amount of neighbors, the concentration of each neighboring node needs to be considered:
1Δt(c(t+Δt,vk)−c(t,vk))=D1dN2·((c(t,h1)−c(t,vk))+⋯+(c(t,hd)−c(t,vk)))=D1dN2·∑hi∈H(c(t,hi)−c(t,vk)).
Since the time scale of CGA is uniform and homogenous, it is possible to assume Δt = 1 and ΔdN = 1 without loss of generality if the nodes in the graph are arranged uniformly. When applying these terms, the previous equation results in:
c(t+1,vk)-c(t,vk)=D·∑hi∈H(c(t,hi)-c(t,vk)).
and by rearranging further the final equation is
c(t+1, υk)=D⋅∑hi∈Hc(t, hi)−︸amount enteringD⋅d⋅c(t, υk)︸amount leaving+c(t, υk).︸current amount
Now it is possible to translate the equation to a value rule usable in CGA. The new concentration of a species s can be calculated with:
ωfcDif(si)=Δfc(υk, si)=fd(si)⋅∑fc(si)∈Mυkfc(si)− fd(si)⋅|Mυk|⋅fc(υk, si)
2.3Parameterizing and scaling
As mentioned in the definition of CGA, the spatial and time scales of CGA are dimensionless and uniform. The scaling factors that result from the true dimensionality of the system (time step size and node distance) have to be included in the value or transition rules, in order to affect the model system.
The diffusion coefficient D (s) represented by fd (s) is the only constant in the diffusion value rule ω (s) that connects the model system with specific characteristics of nature, and therefore provides an the opportunity to scale the diffusion value rule using node distance and the size of the time step. D is measured as a unit of area2 · time-1 and can be retrieved from literature or estimated from the molecular weight or volume. Hayduk and Laudie compiled a list of the diffusivities of 89 small molecules and developed a reliable correlation [28]. Young did the same for 143 proteins [29]. Using these correlations it is also possible to estimate the diffusion coefficient and in turn parametrize the simulation. In case of molecules the coefficient is often given in cm2 · s-1.
The distance between two nodes Δd and the length of a time step Δt has to be specified in order to simulate a defined environment (see Fig. 2). If these parameters are given, the diffusion constant D can be scaled to the size of the system. However, this requires the arrangement of nodes to be uniform across the covered space, so that dG (vj, vk) ∼ dN (vj, vk). We therefore propose the setup work flow depicted in Fig. 3. Ideally, the geometric distance dG is equal for all pairs of neighboring nodes and can therefore be used as Δd. The time step can be chosen depending on the environmental configuration. The final value of D, which is used and applied in CGA, is rescaled to represent Δt and Δd correctly. The scaled diffusivity D¯ is calculated using
D¯=fd(s)=D(s)·ΔtΔd2.
The first step to setup a simulation with cellular graph automata is to define the desired geometry of the system that one wants to simulate. Afterwards, the system is partitioned by covering it with a net-like graph. Each node is responsible for a subsection of space. Further adjustment methods can be applied to truncate and rearrange nodes, so that the true geometry is represented accurately. After the CGA has been adjusted to cover the simulation space, chemical species can be added to the system. Species and their attributes can be retrieved from databases such as ChEBI [35] or Pubchem [34]. For every node in the system the concentration can be set individually, a gradient qualitatively indicates nodes with a high concentration of a particular species in darker color and low concentrations in light color.
2.4Verification
The viability of the simulated diffusion process, calculated by the implementation of the suggested model, is assessed in comparison to a numerical solution of the two-dimensional representation of the diffusion equation [30]. To compare the different approaches, the half-life τh was measured. In this context, τh is the time required for half of the concentration of the steady state to accumulate at a specified position. The half-life was used to contrast both approaches, since this measure is highly delicate and important to approximate the speed of the diffusion process [31]. Therefore, a good consensus between the predicted half-lives indicates a good overall compliance.
The sample system to be simulated was constructed as a square with a side length of 2500 nm. This square is partitioned into two rectangles with a width of 1250 nm (half of the system) and a height of 2500 nm. One of the rectangles is set up to have a starting concentration of 1.0 mol·l-1 and the other rectangle is set to a concentration of 0.0 mol·l-1. The system's initial setup and progression is depicted in Fig. 4. Multiple species have been considered to assess the viability of the system. We have chosen some of the smallest molecules that may be of interest in cellular biology. Those species should be the most critical in the system because large quantities are moving between nodes. The diffusivity covers ranges from 4.40·10-5cm2·s-1 for hydrogen gas up to 6.40·10-6cm2·s-1 for ethane-1.2-diol (seeTable 1) [28].
A: The initial setup of the proposed experiment. A tube is filled with two solutions, separated by a central barrier. One half (indicated with light color) contains a high concentration of the proposed substance, the other half does not contain the solved substance. The distance between the barrier and the point of observation is the diffusion distance, for which the half life will be measured. To start the experiment the barrier is removed. Now the time is measured until half of the equilibrium concentration is reached at the point of observation. B: The initial setup of the rectangular graph automaton with twelve nodes side length. The nodes contain concentrations of 1.0 mol·l-1 (indicated with dark color) and 0.0 mol·l-1 (indicated with light color). C: A schematic depiction of the progression of the diffusion process of methanol at the point of observation. The half life is measured when the concentration reaches half of the equilibrium. This concentration of 0.25 mol·l-1 is indicated with a grey line. The coloring shown in the three boxes illustrate the state of the system at three points in time based on the experimental progression.
Comparison of the simulation results
Species D (s) ( cm2s ) τhCGA (ns) τhNum (ns) Difference (ns / %)
Hydrogen gas 4.40·10-5 135.9 131.8 4.1 / 3.07
Ammonia 2.28·10-5 262.2 254.3 –7.9 / 3.09
Methanol 1.66·10-5 360.1 349.3 –10.8 / 3.09
Benzene 1.09·10-5 548.4 532.0 –16.4 / 3.08
Succinic acid 8.60·10-6 695.1 674.3 –20.8 / 3.07
Ethane-1.2-diol 6.40·10-6 934.0 906.1 –27.9 / 3.08
The graph automata simulation has been performed with 5 ns time steps and 40,000 nodes (200 x 200). The values for the diffusivity have been experimentally determined and are presented in [28].
Initially, a numerical approach was used to simulate the diffusion process in a closed system. This computation was performed using Octave [32]. The simulation uses an explicit finite difference method with a first order upwind in time and a second order central difference in space scheme [30, 33]. To specify the square shape of the simulation space, four reflecting Neumann boundaries were set. After specifying the systems boundaries, the kinematic viscosity of the system is set to exhibit the properties of the desired species ν = D (s). In the simulation, the concentrations of the far right side are observed and the system is simulated until it approaches the steady state c = 0.5 mol·l-1. Finally, the simulated half-life τh is measured.
Additionally, using the definition presented in this paper, a CGA is designed to simulate the same rectangular system (see Fig. 4B). The number of nodes at either side of the grid z is adjusted and the total number of nodes in the graph is |V| = z2. The global size of the system (2500 nm side length) will stay the same, only the distance between nodes Δd has to be recalculated for the scaling of the diffusion coefficient. Different automata were designed to assess the influence of node distance Δd and length of time steps Δt. Therefore 682 different systems have been simulated ranging from 10 to 70 nodes per side (using 31 samples in this range) and time steps of 10 ns to 1500 ns (using 22 samples in this range). Furthermore, these simulations have been performed for all mentioned species.
Simulations for six different substances. The number of nodes (side length of the square graph) ranges from 10 to 70 (implicitly changing the node distance Δd to maintain the overall simulation space) and the time step size Δt ranges from 10 ns to 1500 ns. Each dot corresponds to a simulation performed with different parameters for Δt and Δd. The ratio of the half life τhCGA:τhNum is represented by the brightness of the dots. Dim gray sections with values near 1.0 corresponds to predictions with a low deviation when compared to numerical methods. Half lives that occurred later than expected (values bigger than 1.0) are indicated in darker gray and light gray regions report models that overestimate τhCGA (values smaller than 1.0).
3Results and discussion
A mathematical concept was developed that allows the simulation of multiple chemical species, subject to natural phenomena described by so-called value rules ω. The geometry of the model system is divided into multiple smaller subspaces that are simulated individually (see Fig. 3). Value rules are used to change the concentration of species inside of subspaces of the modeled system. The model itself is scale free, only the value rules have to be adjusted to the actual time and space regime of the simulation.
After the underlying geometry of the simulation is defined, chemical components can be added to each node of the system (see Fig. 3). Different attributes can be assigned to the chemical components that may be subject to change during the progression of the simulation. The diffusion requires the concentration and the diffusivity of each species. The concentration is node specific and will be changed during the simulation depending on the concentration of the surrounding cells, whereas the diffusivity is species specific and remains constant over time. The two global parameters that determine the scaling of the system are species and node independent. Those are the node distance ΔD (spatial step size) and the time step size Δt. Following the initialization of all required parameters, the simulation can be started. In each time-step the transition rules are applied and new values are set for the next iteration. A step-by-step progress of the setup of such a system is reenacted in Appendix A and another example for the implementation of value rules in the case of first order reactions is given in Appendix B.
The simulation system and model were implemented in order to verify their applicability. We developed the application programming interface Simulation of Natural Systems using Graph Automata (SiNGA) in the Java programming language. The source code is provided on GitHub under GNU General Public License Version 3 (see github.com/cleberecht/singa).
The results of an exemplary system (see Fig. 5) indicate, that the simulation using CGA with an increasing number of nodes and a decreasing time step size converge to the half life calculated with the numerical simulation. However, the graphs also show that the system is unstable when a large number of nodes (equivalent to small node distances Δd) is used in conjunction with large time steps. This is to be expected if the combined amount of concentration to be distributed among the neighbors in one time step is larger than the concentration a node currently contains. Hence, the time scale is underestimated and negative values ensue. Consequently, the initial setup of the system has to be done carefully. The dimensions of the system have to match the speed of the species with the highest diffusivity D (s). We derived the following threshold
Δd2Δt>maxv∈V(deg(v))·maxs∈S(D¯(s))-maxv∈V(Δc(vi,vj)),
that traces the arches that can be seen in Fig. 5. Here, let maxv∈V(Δc(vi,vj)) be the maximal difference in concentration between two neighboring nodes. Additionally, the node with the maximal degree and the species with the highest diffusivity are taken into account. If the parameters of a CGA do not salsify the inequality, the system is unlikely to reach a meaningful result. As a result, this inequality approximates the stability of the global system, leading to a rather pessimistic prediction that resembles the worst case scenario of a possible configuration. By inserting the actual values of a proposed CGA simulation into the inequality, adjustments can be made to create a stable system. The geometric setup of the system can be changed in two different ways. On the one hand, it is possible to reduce the globally highest node degree. On the other hand, species with high diffusivity may be removed, or steep concentration gradients can be smoothed across multiple nodes. If the system setup is to be taken as fixed, the environmental parameters Δd and Δt can be adjusted to increase stability. Smaller time steps entail more calculations in intermediate steps to stop values from changing too rapidly. Increasing the number of nodes has the same effect. When the size of the time step approaches zero and the number of nodes reaches positive infinity, the predicted half life of calculated with CGA approaches the result gained by classical numerical methods. The system gets more accurate when small time steps are used in conjunction with small node distances. Simultaneously, the runtime of the simulation increases.
As depicted in the flowchart in Fig. 5 for every time step every node needs to be addressed at least once. The complexity of each time step is O(n2) , dominated by the number of nodes |V| and number of species |S|. Conclusively, the end user needs to find a trade-off between accuracy and time complexity depending on the requirements for the simulation. To gain a brief overview of the system's behavior an inaccurate setup might suffice. If the diffusion process needs to be determined accurately, more nodes and small time steps are required. Finally, the half life τh calculated by classical numerical simulations and those from CGA are compared in Table 1. Remarkably the difference between both methods amounts to about three percent across all species.
4Conclusion
PDEs are an established strategy to simulate a variety of natural systems. In systems that have predictable behaviors and outcomes PDEs flourish to their full potential. In biology however, one often encounters systems that are very complex and influenced by multiple aspects. In these cases PDEs reach the limits of their applicability. Using implicit systems such as CA or CGA, it may be possible to simulate different systems that cannot be tackled efficiently using PDE.
With the proposed definition of CGA we have shown that it is possible to simulate diffusion of different chemical species to a high degree of accuracy. Diffusion is one of the most fundamental processes that many biological systems rely on. The system shown here is able to easily adjust to different time and space scales with little adjustments to the configuration of the system. Using the underlying structure of graphs it is possible to define different topologies. It is possible to add plenty of species to a simulation. Furthermore, the user is able to simulate and observe the system in order to improve the understanding of its current behavior. It is even possible to alter the concentration of a species at a specific node, or the structure of the graph at any point during the simulation, due to the implicit definition. Finally, not much mathematical understanding that is needed to set the system up (see setup process in Appendix A). As shown in Fig. 2, the user has to initialize the graph first, than choose the required species and finally define the systems parameters Δd and Δt. To guide the definition process of the parameters, the threshold (Equation 4) can be consulted. A trade-off can be chosen between accuracy and time complexity of the simulation. Hence, the end user can decide whether qualitative predictions are sufficient or precise simulations are required. Databases such as PubChem, ChEBI, or UniProt allow the automatic extraction of features for different species that are relevant for the estimation of critical parameters (such as the diffusivity) [34–36].
Computer simulations are able to act as a bridge between theory and experiment [37]. In the past the gap between theory and experiment for molecular behavior has been overcome by molecular dynamic simulations [38, 39]. However there is still a lot to be done to bring theory and experiment together when it comes to the dynamics of cellular processes. First steps were done by many researchers over the past centuries. Nevertheless, the gap between generalizable simulations and experimental outcome still needs to be closed. We hope that the different fields of science will work together to make a similar approach to "Cell Dynamic Simulations"possible.
In the near future, research will be directed towards the creation of value rules for different chemical reaction types and membrane transport. The setup process for simulations will be further simplified by providing possibilities to extract information from relevant databases and by offering visual feedback using the graphical user interface. Additionally the SiNGA application programming interface (available on GitHub github.com/cleberecht/singa) is under constant development.
All authors designed the research. C.L. designed and implemented the model and simulation strategy, and evaluated the performance. C.L. and F.H. wrote the paper.
Appendix A. Simulation setup
Step 1: Definition of the target system. The layout of the underlying graph of the CGA is the first step in the setup of a simulation. The geometry and dimensionality of the target system has to be respected and eventually assumptions have to be made. A one dimensional system can be simulated by using a line of nodes, where each node is only connected to the next node. By also connecting the first and the last node of the system a periodic boundary condition in terms of regular cellular automata can be introduced. A two dimensional system can be composed in different ways, for instance by arranging four nodes around a central node (see example system in Fig. 4), a classical cellular automaton with a squared tiling can be recreated. It would also be possible to create a hexagonal tiling by introducing six neighbors to each node. Again, by connecting opposite sides of the system periodic boundary conditions are introduced. In theory the modeling of arbitrary dimensionalities should be possible depending only on the connection of nodes in the graph.
Example: For the purpose of this guide, a two dimensional system is chosen without periodic boundary conditions.
Step 2: Placement of the corresponding nodes. If the CGA should represent the actual geometry of a cell, a microscopic image can be used as a guideline to place the nodes of the graph. The number of nodes that are supplied in this step determine the accuracy of the system to a large extend. Each node is responsible for the simulation of a small region of space during the simulation. More nodes increase accuracy as well as runtime. Since the nodes need to be placed uniformly in the desired space a relaxation algorithms such as Lloyds Algorithm [40] should be applied and afterwards the nodes should be connected using a stringent distance cutoff. After this step the graph should uniformly span across the simulation space. Now the average distance between neighboring nodes is used to parametrize Δd.
Example: A simple square simulation space with an area of 100 mm2 is filled with 100 nodes. The large square is partitioned in 100 small squares, and at the center of each square a node is placed. Now the space is uniformly covered. Afterwards, neighboring nodes are connected and the distance between two nodes should be uniformly the same with Δd = 0.9 mm. The distance might seem surprising but is a result of the nodes being placed inside of the square and not on the border.
Step 3: Species selection and concentration assignment. Now the species of interest need to be specified and the concentrations have to be set. Each node requires a starting concentration.
Example: We might choose the molecule Benzene that has a concentration of 0.5 mol·l-1 in the two leftmost columns. Hence we set the value function fc (Benzene) = 0.5 for the corresponding nodes and fc (Benzene) = 0.1 for all remaining nodes.
Step 4: Choosing Δt and determining D¯ . If we want to simulate the diffusion of Benzene its diffusivity has to be set as well. To scale the diffusivity for the proposed setup system, the size of the time step is required. To choose the time step size most suitable for ones requirements, the proposed threshold (Equation 4) will be consulted, with the already determined values inserted.
Example: For the system that was introduced up to this point, the following threshold can be derived:
0.92Δt>4·D¯(Benzene)-0.4
A node is neighbored to a maximum of four neighbors, the node distance has been set to 0.9 mm, and the maximal difference in concentration is 0.4 mol·l-1. Now the following three time steps will be considered: 1 s, 50 s and 100 s. To scale the experimentally determined diffusivity D (Benzene) = 1.09·10-5cm2·s-1 [28] to D¯(Benzene) , Equation 3 is calculated for each proposed Δt and inserted into the threshold (D is brought to the same unit). This insertion results in the following inequalities: 0.81 > -0.394 for 1 s, 0.162 > -0.131 for 50 s and 0.0081notgreaterthan0.136 for 100 s. The time steps 1 s and 50 s are sufficient for a stable system, but a time step of 100 s would be too large. The larger the absolute difference between both sides of the inequality, the more accurate the resulting simulation.
Simulation. After the graph is constructed and the the time step size Δt, node distance Δd, and scaled diffusivity of all desired species are set, the simulation can begin. During simulation, the change for each node is calculated first using the the value rules ω. After all changes have been calculated, they are added to the previous values and the time step is increased.
Appendix B. Implementing value rules
The implementation of additional value rules is dependent on their requirement for neighboring values. If the value rule does not require information from neighboring values, its implementation is straight forward. As an example a simple case of chemical kinetics shall be demonstrated:
The general case of a first order reaction with two chemical species A and P and their stoichiometric coefficients a and p can be denoted in the form:
aA→pP
The reaction rate of a first-order reaction A → P can be described by:
v=-1adc(A)dt=1pdc(P)dt=kc(A)
for which:
• v is the reaction rate (in mol·l-1·s-1),
• c (S) is the concentration of a species s,
• k is the rate coefficient, and
• t is the time.
The differentials will be be transformed to discrete changes, to transition to CGA.
v=Δc(S)Δt=1pΔc(P)Δt=-1aΔc(A)Δt=kc(A)
Further, the concentration will be rewritten to c (s, t), to describe c as a function depending on species and time:
1ΔtΔc(s,t+Δt)=1p1ΔtΔc(P,t+Δt)=−1a1ΔtΔc(A,t+Δt)=kc(A,t)
Because of the uniformity of the time steps Δt can be set to 1:
Δc(s,t+1)=1pΔc(P,t+1)= −1aΔc(A,t+1)=kc(A,t)
Therefore the recurrence relation for the new concentration of a species S at t + 1 in a first-order reaction can be calculated with:
c(s,t+1)={c(s,t)+k·u(s)·c(A,t) forproducts,c(s,t)-k·u(s)·c(A,t) forsubstrates.
In this equation u (s) denotes the stoichiometric coefficient in the reaction that is to be simulated. The equation can be translated to a value rule in CGA notation, for which only the change is relevant:
ωfcKin(si)={fk(si)·u(si)·fc(sA) for products,−fk(si)·u(si)·fc(sA) for substrates.
Note that the rate of change is always calculated in dependence of the substrate concentration of the reaction sA, since if there is no actual substrate no reaction can occur. The rate coefficient k from literature or databases needs to be scaled to take the actual time step into account, that is to be applied in the concrete CGA with k¯=fk(s)=k(s)·Δt .
This work was supported by the European Social Fund (ESF) and the Free State of Saxony, Germany. We would like to thank our colleagues, especially Sebastian Bittrich and Florian Kaiser, for thought-provoking impulses and fruitful discussions. Additional we thank Hannah Siewerts for proofreading and feedback on the manuscript.
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Management is one of the most important aspects of the production house. The production house needs to manage the entire project flawlessly. The work, task, logistics etc have to well planned and executed by the production house.


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text:
Il campionato mondiale di pallavolo maschile 1960 si è svolto dal 28 ottobre all'11 novembre 1960 a Rio de Janeiro, in Brasile: al torneo hanno partecipato quattordici squadre nazionali e la vittoria finale è andata per la terza volta all'URSS.

Prima Fase
Le prime due squadre di ciascun gruppo vengono inserite in un girone finale da 10 squadre per determinare le posizioni dalla prima alla decima. Le nazionali di Stati Uniti e Francia, uniche due squadre inserite nel gruppo E, sono ammesse entrambe nel girone finale a 10 squadre.
Le ultime di ciascun gruppo vengono inserite in un girone finale a 4 squadre per stabilire le posizioni dall'undicesima alla quattordicesima.

Gruppo A

Gruppo B

Gruppo C

Gruppo D

Gruppo E

Seconda Fase

11º-14º posto

1º-10º posto

Classifica finale

Pallavolo nel 1960
Campionati mondiali di pallavolo maschile

redpajama_set_name: RedPajamaWikipedia


text:
FighterSweep Interviews Bremont Co-Founder Nick English
FighterSweep Staff 1 Comment Air Force, Interview, Marine Corps, Military Aviation, Navy
FighterSweep and its parent company, Force12 Media, have recently launched a parternship with Bremont Watch Company. Bremont is now the official time keeper of Fighter Sweep and Force 12 Media.
FighterSweep was lucky enough to sit down with Bremont co-founder Nick English to get his thoughts on the new partnership and how the Bremont Watch Company has been a favorite of military pilots.
Bremont has been creating special bespoke watches for military crew and squadrons for almost a decade. Its timepieces are built to withstand the same level of rigorous forces placed on the aircraft and pilot.
A great storyteller and an accomplished pilot in his own right, Nick and FighterSweep had a lot to talk about.
FS – Nick, can you quickly tell us about Bremont and how you became involved with Force12 Media and Fighter Sweep?
Bremont really started at an early age for my brother, Giles, and myself. We had this wonderful upbringing spending most of our time in our father's workshop where he built everything from aircraft, cars, to musical instruments. He also built a sailing boat that we went to live on as children.
One of his passions was also watches and clocks – basically anything mechanical. His passions included restoring old clocks and he'd buy one from an auction and get us to help restore it as children.
As we grew up, our father did a lot of flying, especially in vintage 1940's aircraft. Our family did a lot of air-show flying. Life changed for us in 1995 when my father and I were in a plane crash, whilst practicing in a 1942 T-6 Harvard for a formation routine.
My father died and I broke over 30 bones and was in intensive care for many months. When I recovered, Giles and I agreed life is very short and wanted to do something we both loved doing, so that's exactly what we did.
Euan English, Nick and Giles Father. Courtesy: Bremont
We decided to make watches. We knew Britain had an incredible history for watch-making and we wanted to help re-establish it. It was five years until we launched our first watches onto the market in 2007. It's very much created out of passion for beautifully engineered product, and a lot of sweat and tears!
The connection with Force12 and Fighter Sweep happened very organically. Just out of interest for what each party was doing, Bremont's military watch division and Fighter Sweep started sharing interesting content on social media. Very quickly we realized we had a lot in common and shared many of the same enthusiast base.
FS – Why do you think that Bremont Watch Company has become such a favorite of the military, especially military pilots?
Bremont is a brand born from aviation and a love of all things mechanical. Our father and both Giles and myself were both sponsored through University by the Air Force and we genuinely have a huge appreciation and interest in what the military do.
What is interesting is that the majority of military we talk to share very similar passions to us. They fully appreciate what goes into a beautifully engineered product, whether it be a beautifully engineered aircraft, firearm, motor-car or wrist watch. A well maintained aircraft from the 1940's will work as well as the day it was built, and the same applies to a mechanical time piece.
What I do love about the military watches we manufacture is the kin-ship that goes with it. There is an immense sense of pride in the squadron, regiment or military unit they come from. This passion needs to be reflected in the product itself. They are under no doubt whatsoever that they are getting something really rather special and unique when they receive their timepiece.
FS – There are a lot of watch companies that like to sell to military members, especially pilots. What sets Bremont apart?
I totally agree. There are some lovely brands out there, all doing slightly different things. When you look at it in a little more detail, I actually believe there are a few things that differentiate Bremont from other watch companies.
I think having an aviation background and a small exposure to military life gives us a different outlook to other brands when we are producing watches. Not many brands take this area of their business as seriously as we do. It is not about just sticking a logo on a dial – it about much more than this, and you can see it very clearly when you see some of the projects we have done over the last few years.
To achieve this, I have to say, we do have a very special team internally at Bremont who focus on nothing but military and special projects (counter terrorism etc). Not many watch companies can boast about having an F-15 flying ex-USAF Colonel in their team! The respect for what the military do therefore goes without saying at Bremont.
The big difference comes down to the product itself. We only make mechanical chronometer rated watches. They are all manufactured in the UK. Many of our watch parts are made at our facility in Silverstone in the UK.
Bremont co-founder Nick English enjoys the view over Oxfordshire from the cab of the Sea King Mk4. Courtesy: Bremont Military
If you ever visit there you will literally see a bar of steel going in one end of the factory and a watch case or watch part coming out of the other end. If you then come to Henley-on-Thames, you will then see rows of specially trained watch makers assembling the watches individually.
We make a finely tuned mechanical machine that a military member can wear with pride and really appreciate. It tells something about them. We take pride in the fact that our watches are all mechanical, meaning they don't have a battery. We will never make an inexpensive quartz watch. We joke that a battery powered quartz watch has no heart or soul!
We go to extra lengths to put the DNA of our customer's jet, squadron, or organization into our watches. We take one of our core line and make modifications so the watch is very special to the group that commissions it.
For example, our KC-135 watch has a 24 hour Zulu hand marked with the colors of the air refueling boom, or the rotor on the back of the watch for an A-10 squadron which is designed to rotate and look like their very unique Gatling gun. Not many other brands go to that level of customization.
FS – You seem to have really integrated with military culture and understand your unique customers. How does a British Luxury brand manage to do that?
The first every military watch we did was for the US Navy Test Pilot School together with the Empire Test Pilot School in the UK. These projects started close to 10 years ago and we are still making watches for them!
This was all happening at much the same time we started working with the British Ejection Seat manufacturer, Martin-Baker (MB). This partnership organically brought many US Navy and Marine pilots (who sit on Martin Baker seats) into the Bremont fold.
Photos courtesy Bremont Military
Martin-Baker have saved over 7,500 lives to date, which is an incredible statistic. To work with MB our watches had to go through the same testing as their seats themselves. We learnt a huge amount from this testing programme and the Bremont MBII was born – a watch that was very durable and great looking.
If you see anyone wearing a Bremont MB watch with a red-barrel on it, it means they have punched out of an aircraft! They all have such a special story attached to them.
Further to this, we started to recognize that the Bremont brand was being noticed by more military when a U-2 pilot saw one of our watches on the wrist of Bear Grylls, a former SAS Special Forces member who had a TV show called "Man vs Wild". He asked that we produce a watch for their U-2 Spy Plane Squadron at Beale AFB in California. Wearing the watch on the outside of the space-suit, we could also prove to them that during the MB Testing programme, the watch had been subjected to -50 degrees C at 100,000 feet!
A U2 pilot and his Bremont, Photo credit: Bremont military
Our more recent partnership with aerospace giant Boeing has further validated us as a brand that military trusts and respects.
We became acquainted very early on with a veteran US Air Force F-15C pilot who was a big collector of mechanical watches and recognized what we were doing. He was one of the first fighter pilots to wear Bremont and quickly became our unofficial consultant on military related topics. When he retired from the military, we brought him on officially within the brand. We understand how important it is to "get it right" with our military customers.
Lastly, we like to think that we provide a customer service to our military clients that is second to none. The team is outstanding, they really are. We understand how busy and stressful a military lifestyle can be, so we strive to be efficient and responsive to all enquiries or concerns. At Bremont, we never think a military customer should be honoured to wear our watches, rather it is us who are genuinely honoured that they choose to wear Bremont!
FS – It is very exciting hearing a little more about the Bremont brand. Any last words Nick about what the future holds?
We are seeing our military side of the business grow each year which is wonderful, and something of that we are immensely proud. It is all very organic which makes it that much more special.
Air to Air refueling. Photo Bremont Military
The ideas that military members come to us with are fantastic and many times end up being incorporated into civilian watch models.
Our 2016 celebration of Boeing's 100-year anniversary is also very exciting, and we have built a limited edition of only 300 pieces for them to help celebrate this incredible milestone. The Boeing connection was always very material research led, and hopefully you can expect some other interesting developments on this!
All I would say is that if you have any questions you would like to ask about this side of the business please do send a note to [email protected] and they will quickly get back to you. You must also follow them on social media (@bremontmilitary) – there really are some wonderful photos and stories being posted.
FighterSweep is excited about the new partnership. Get your official FighterSweep time hack from the Bremont watch above! (Mobile users at the bottom of your scroll)
Top Photo: Bremont co-founder Nick English with the 1954 Max Holste Broussard, affectionately known as the "Bremont Bus". Photograph courtesy of Andy Wilson.
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Character actor
Television actor
Chabot College
American actor and producer
Samantha Lewes[1978-1987]
Rita Wilson[ M. 1988]
Tom Hanks is a well known actor across the globe. He hails from the country of the United States of America. Apart from being an actor Tom Hanks is also an accomplished filmmaker.
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Karon Riley
Tom Hanks was born on the 9th of July, 1956 in the city of Concord located in California, having graduated from Chabot College and the California State University.
Tom Hanks has been married twice, first to Samantha Lewes, it was with her that he has two children, Colin and Elizabeth Hanks. Post the divorce Tom Hanks got married to Rita Wilson. The couple together have two sons.
Tom Hanks is particularly known for his performances in dramatic and comedic films such as Big (which released in 1988), Splash (which released in 1984), Turner & Hooch (which released in 1989), Sleepless in Seattle (which released in 1993), A League of Their Own (which released in 1992), Apollo 13 (which released in 1995), The Green Mile (which released in 1999), You've Got Mail (which released in 1998), Cast Away (which released in 2000), and Road To Perdition (which released in 2002).
Later in the current decade Tom Hanks is credited with films such as Captain Phillips (which released in 2013), Cloud Atlas (2012), Saving Mr. Banks (which released in 2013), Sully (which released in 2016). Apart from this, Tom Hanks has also appeared in the Hon Howard directed film series based on Dan Brown's novels, where Hanks portrays the role of Robert Langdon, these films include The DaVinci Code, Angels & Demons and Inferno.
Tom Hanks' impressive work portfolio extends to animated films as well, where he lends his voice to the character of Sheriff Woody, who is part of the Toy Story movie series. Tom Hanks' collaboration with director Steven Spielberg is also an impressive one, with five such films being made by the duo, those include Saving Private Ryan (which was released in 1998), Catch Me If You Can (which was released in 2002), The Terminal (which was released in 2004), Bridge of Spies (which was released in 2015), The Post (which was released in 2017).
Tom Hanks has won the Golden Globe Award and the Academy Award for Best Actor multiple times, first for his role in Philadelphia (which was released in the year 1993) and then again for his 1994 release, Forrest Gump. This feat helped Tom Hanks become the second actor in history to have won the Academy Award for two consecutive years, the other actor being Spencer Tracy.
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Michigan is the third largest producer of Christmas trees in the nation, with 700 tree farms producing an average of three million trees a year. Not only are we a top producer, but we also grow more varieties than any other state.
Whether your family is starting a new Christmas tradition or one that's been in the family for years, selecting the season's Christmas tree is a memorable experience for the entire family. Where you choose to purchase your real Christmas tree depends on what kind of experience you're looking for this holiday. Fortunately, we're not short on Christmas tree farm options in Michigan.
If you want to take your family on an exciting Christmas adventure, we suggest spending a day at a choose and cut farm. Choose and cut farms involve exactly what you think; you choose a tree, cut it down, and bring it home to decorate. You can find our favorite choose and cut farms in Michigan, here.
If you want a little less adventure, visiting a retail lot is another great option. Retail lots offer a wide selection of pre-cut Christmas trees while still preserving much of the real Christmas tree buying experience. You can find a list and map of our favorite retail lots, here.
Most farms open the weekend after Thanksgiving, dubbing it "Green Friday." Typically, farms provide saws if necessary and will trim and package your tree so it's easy to transport home. Prices and types vary farm to farm, so if you're looking for a specific price, size, and species it's best to call ahead.
Similar to visiting pumpkin patches and apple orchards in the fall, many Christmas tree farms come complete with hot chocolate, tasty treats, festive decorations, and sometimes Santa visits and sleigh rides. The winter activities available are unique to each farm.
After you find your perfect Christmas tree, make sure you get a fresh-cut (the process of removing a 1/2" thick disc of wood at the base of your tree) and place it in water as soon as you get home; this will keep your tree fresh for the entire season.
If you're still on the fence about whether to decorate your home with an artificial or farm-grown tree this season, we recommend going to explore one of the many tree farms Michigan has to offer and discover what is best for your family. We list each farm's features, hours, and opening weekends on our website.


Walter cleaning systems deliver efficient and effective cleaning, consuming a minimum of water and chemicals. A large part of the efficiencies are derived through the use of the Walter chemical injectors.
Designed to make the cleaning process as simple as possible, changeover between cleaning stages is as simple as turning the lever and selecting the correct lance. Self-explanatory symbols on the injector units help avoid confusion for the user. Non-return valves prevent chemicals and water from entering the air line.
Precise dosing control is imperative to maximise the efficient use of water and cleaning agents. This control also ensures continuously fine-porous foam. Walter chemical injectors allow separate dosing of one or two chemicals, each of which is continuously adjustable (from 0.5% to 12%) – minimising wastage of water and cleaning agents.
The extremely robust Combijector is ideal for accurate dosing of one locally stored chemical. The single selection lever is user friendly and can change operation from pressure cleaning to foaming / disinfection quickly and simply. The compact, lightweight unit can be mounted in-line for simple installation. Water pressures 3 – 300 Bar. Separate chemical dosing, continuously adjustable from 0.5% to 12%. Manufactured in 316 stainless steel.
Accurately dose up to two chemicals with a single selection lever - perfect for stations which require both foaming and disinfection functions, alongside pressure cleaning. These wall mounted hygiene units can be used with locally stored or centrally controlled chemical systems. Water pressures 3 – 300 Bar. Separate chemical dosing, continuously adjustable from 0.5% to 12%. Manufactured in 316 stainless steel.


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Oswego County
Traveling NY Shipwrecks Exhibit In Oswego
January 14, 2015 by Editorial Staff Leave a Comment
The Great Shipwrecks of NY's Great Lakes is in Oswego, NY, at the Tyler Art Gallery in Penfield Hall Library at SUNY Oswego. The exhibit was developed for the 2014 Great New York State Fair and was updated for this installation. It will be on display through January 22, 2015.
The exhibit includes interpretive panels highlighting shipwrecks in Lake Ontario, Lake Erie, Lake Champlain, the Finger Lakes, Lake George and the St. Lawrence River; videos; and a newly-built replica of the 'turtle ship' Radeau that sunk in Lake George. Freshwater science technology components including a remotely-operated underwater vehicle and a Great Lakes Research Consortium in-water sensing buoy. [Read more…] about Traveling NY Shipwrecks Exhibit In Oswego
Filed Under: History, New Exhibits Tagged With: Maritime History, New York Sea Grant, Oswego County, Shipwrecks, SUNY Oswego
Soldiers' Tales from an Old Cemetery in Oswego County
November 11, 2014 by David Fiske 1 Comment
There are a number of tombstones in the Feeler Family Cemetery in the Village of Cleveland in Oswego County, but two stand out.
Unlike the other twelve grave markers, these two are inscribed with the names of the deceased. Both of the men whose graves are marked were African Americans, and both served in the Army during the Civil War. [Read more…] about Soldiers' Tales from an Old Cemetery in Oswego County
Filed Under: African American History, History, Military History Tagged With: Cemeteries, Civil War, Columbia County, Oswego County
North Country Teacher Taught Southern Freedmen
September 4, 2014 by David Fiske 1 Comment
Back-to-school time perhaps brings back, for adults, the memory of a favorite teacher. But of those who are so warmly remembered, how many can elicit this wish by a former student of a 19th century teacher?
"If I could be permitted, how gladly would I again fill up the wood-box in your room and kindle the fire on your hearth…"
Those words came from the prestigious African American preacher, Rev. Daniel Webster Shaw (who, interestingly, was the son of a former slave, Harriet Shaw, with whom Solomon Northup was acquainted in Louisiana). "If I have done anything, or come to anything worth while, it is all mainly due to your timely helpfulness and godly admonition," Shaw wrote. "I think of the school days on the Tache [Teche, a bayou in Louisiana], and all the kind ways in which you helped me to start out in life." [Read more…] about North Country Teacher Taught Southern Freedmen
Filed Under: African American History, History Tagged With: Abolition, Fulton County, Oswego County, Political History, Religion, Slavery
Chester Sanders Lord of the New York Sun
February 3, 2014 by Lawrence P. Gooley 1 Comment
Modern media includes television, radio, newspapers, and Internet sources, together bringing us news from local to international. But until about a century ago, newspapers did the job. By the mid-1800s, the process of delivering timely news to the nation's dailies was achieved, courtesy of the telegraph. It wasn't until the 1920s when other forms of media (radio and newsreels) began carving their own niche in reporting the news.
When newspapers ruled, editors wielded great power and thus bore great responsibility. Ethics were critical but weren't always adhered to. It took men of courage to do what was right, and among the best of them was Chester Sanders Lord, a man with roots firmly embedded in northern New York State. [Read more…] about Chester Sanders Lord of the New York Sun
Filed Under: History Tagged With: Finger Lakes, Hamilton College, New York City, Oswego, Oswego County
John Donovan: Buried Twice in a Month
August 27, 2013 by Lawrence P. Gooley Leave a Comment
In a tragic story compounded further by a shocking turn of events, a North Country woman once buried her husband twice in less than thirty days. Admittedly, that seems impossible without some sort of extramarital shenanigans going on, but that wasn't the case. In fact, there were actually three burials in the story within that short span of time, capping a series of highly unlikely occurrences. To complicate matters even further, the woman actually had only one husband.
Before reading further, if you like solving puzzles, read that paragraph again and try playing detective. How could all that be true? At this point, everyone should be sufficiently confused and anxious for an explanation. And here it is. [Read more…] about John Donovan: Buried Twice in a Month
Filed Under: History Tagged With: Adirondacks, Genealogy, Oswego County
North Country Oddity: Dr. Dunlap of Watertown
September 4, 2012 by Lawrence P. Gooley Leave a Comment
Out of Europe in 1872 came a cable from Doctor John L.Dunlap of Watertown, informing his hometown friends that Louis Thiers, president of France, had welcomed and befriended the North Country's most prominent physician and statesman. So impressed was Thiers with Dunlap's support of the common man that, according to the doctor's telegram, a statue was to be erected in his honor.
A detailed description of the sculpture was provided, to be done in the finest Carrara marble and placed in the Capitoline Museum in Paris or "beside that of the Apollo of the Belvidere in the Vatican at Rome." In keeping with Dunlap's politics, the sculpture's inscription was to read, "The will of the people is the supreme law."
The cost of commissioning Cordier was placed at nearly $70,000 for the five-year job, and the unveiling was scheduled for March 4, 1877—the day John Dunlap planned to be sworn in as America's 19th president. Now that's advertising.
Yes, it was all starting to sound a bit bizarre. On the other hand, it may have been a clear-minded effort aimed at self-promotion, truly the doctor's forte.
Raising the bar a bit, Dunlap had begun claiming that he was engaged to Queen Victoria. In July 1873 was held the grand opening of the Thousand Island House, a spectacular hotel at Alexandria Bay. Since it was the social highlight of the summer season, Dunlap informed the media that he would be in attendance—and planned to meet Queen Victoria there.
The event was huge, with an estimated 10,000 visitors. Dignitaries from across New York State and Quebec were invited to the gala, and some did attend. Newspaper coverage humored readers with a report on Dr. Dunlap's appearance.
"The doctor came down from the city for the purpose of meeting Queen Victoria, who, from some unexplained cause, did not arrive. Several scions of English nobility were introduced to the Doctor and were much pleased with his scholarly attainments, his commanding figure, and splendid personal appearance, as well as the extempore remarks made by him on that occasion. The Doctor wears next to his heart a beautiful likeness of the Queen, presented by her at the time of their betrothal."
Did this behavior suggest a mental problem, as some have claimed, or was this just an old man (he was 74) having a lot of fun and enjoying the attention?
In early 1874, Dunlap was taken ill, but managed to recover and mount another run for governor. The Watertown Times offered its support, noting that "The Doctor was swindled out of his matrimonial engagement with the British Queen and cheated out of the Presidency, and yet it is said he will accept the office of Governor of the Empire State."
At the July 4 celebration at Sackets Harbor, General Grant was expected to speak (he had served two stints there). Dr. Dunlap was invited to give another of his stirring talks, this time on Stephen Douglas, Lincoln's famous debate opponent.
In August of that year, the newspapers had more fun with this report: "We are informed that Alexander, Emperor of Russia, has abdicated in favor of Hon. John L. Dunlap of this city, who will henceforth be known as Emperor John the First."
At the time, it may have been all in good fun. Dunlap was a likable guy and unabashedly open, providing great copy for newspapermen. After all, his medicinal claims, political forays, decades of seeking the presidency, and supposed connections to foreign leaders were very entertaining.
Viewed 150 years later, they suggest an oddball character, and maybe someone not playing with a full deck. But perhaps the truth lay in his love of attention, his devotion to politics, and his great talent for promotion. What seemed eccentric or erratic may well have been a carefully contrived personal marketing plan.
Whatever the case, it worked. Throughout his life, John Dunlap was prominent in the media, a successful physician, and financially well-off from the sale of his medicines. In December 1875, he died at the home of his son and daughter in Parish (Oswego County). His estate was valued at about $30,000, equal to approximately a half million dollars today. He apparently was doing something right all those years.
Four days after his death, the Jefferson County vote totals from the most recent elections were published. True to form right to the end, Dunlap had received a single vote for Poorhouse Physician, tied for last with "Blank" (representing a blank ballot) behind four other doctors.
There's no doubt that John Dunlap was an unusual man. His contemporaries referred to his "harmless idiosyncrasy" and his fervent love for and involvement in politics. They smiled at his loquaciousness, his many love letters to the queen, and his insistence that the people truly wanted him as president, but that political parties had constantly foiled his efforts.
Even at his death, there were those who suspected he was perhaps crazy like a fox, as indicated in one writer's eulogy. "And yet, despite these singular mental aberrations, the doctor was a moneymaker. He would never pay anything to advance his political or marital schemes. Herein was ground for the belief of many that the doctor only feigned his peculiarities, the better to be able to sell his medicines, for no matter with whom he talked on the subject of politics or the like, he was sure before the end of the conversation to pull out a bottle of his medicine, urge its efficacy, and try to make a sale."
John L. Dunlap—tireless salesman, dyed-in-the-wool patriot, presidential aspirant, and Watertown legend—truly a man of the people.
Photo: Notice of Dunlap's appearance at Alexandria Bay (1873).
Lawrence Gooley has authored eleven books and dozens of articles on the North Country's past. He and his partner, Jill McKee, founded Bloated Toe Enterprises in 2004. Expanding their services in 2008, they have produced 24 titles to date, and are now offering web design. For information on book publishing, visit Bloated Toe Publishing
Filed Under: Uncategorized Tagged With: Jefferson County, Lawrence Gooley, Medical History, Oswego County, Political History
Fort Ticonderoga Acquires 1759 Powder Horn
December 8, 2011 by Editorial Staff 1 Comment
Fort Ticonderoga's collection is strengthened by a recent donation of an engraved powder horn made in 1759. The horn is inscribed "JOSEPH STAB HIS POWDER HORNE 1759." Joseph Stab's identity thus far remains silent. A search of available records for the military campaigns of 1759 has not yet revealed who he was.
Stab's powder horn is nicely engraved with a variety of scenes and images. Directly above his name is a hunting scene depicting a horseman and three hounds chasing a deer. Another part of the horn is engraved with what appears to be Indians in trees shooting at game. A variety of birds, trees and deer are depicted over much of the remainder of the horn along with depictions of sailing ships one of which is identified as "Sloop Oswego." The British Navy sloop Oswego was constructed on Lake Ontario in 1755 and captured (burned) by the French on August 14, 1756 at the end of the siege of Fort Oswego. Was the sloop depicted on Stab's horn as a memory of service in a previous military campaign? Further research may reveal the answer.
Powder horns were regularly issued to American provincial and British regular soldiers in the French & Indian War for carrying bulk gunpowder. Unlike what is commonly seen in the movies, soldiers generally did not load their muskets directly from a horn. The horn was a container in which to carry bulk gunpowder to later be used in making paper cartridges. Many soldiers had their horns engraved perhaps as a way of commemorating their military service. Although there is little direct information that survives regarding the process of engraving a powder horn, it appears from scant evidence that most horns were engraved by a only a handful of men, perhaps individuals with known artistic or engraving skills, serving as fellow soldiers in the army. Some powder horns have poetic phrases reflecting upon specific events and military campaigns; others are inscribed with only the owner's name and date. Many powder horns have maps or floral or naturalistic scenes engraved on their surfaces. Each horn, however it is decorated is a unique record of a person's military experience.
Fort Ticonderoga's collection of 18th-century military objects is celebrated as one of the best of its type in the world. The collection of engraved powder horns numbers about seventy-five pieces spanning the French & Indian War and American Revolution. According to Chris Fox, Fort Ticonderoga's Curator of Collections, "Each powder horn is unique and has a story to tell."
Dozens of engraved powder horns are exhibited in the museum each season and many will be featured in the museum's newest exhibit Bullets & Blades: The Weapons of America's Colonial Wars and Revolution opening May 2012.
Filed Under: Military History Tagged With: Fort Oswego, Fort Ticonderoga, French And Indian War, Maritime History, Material Culture, Oswego County
War of 1812: Carrying the Great Rope
October 11, 2011 by Lawrence P. Gooley Leave a Comment
During the War of 1812, control of Lake Ontario was one of many issues considered critical by both sides. A key position for the British was Kingston, Ontario, about thirty miles north of the vital American base at Sackets Harbor. In an effort to establish domination of the lake, the two sites engaged in a shipbuilding race.
The British finished first and gained control, but American builders quickly completed three new ships (two brigs and the huge frigate Superior, larger than its British counterpart). Their launch required only weapons and rigging, which were en route from Brooklyn via Albany. In 1814, hoping to keep those vessels in port, the British sought to disrupt American supply routes. A prime target was Fort Ontario, located at Oswego on the mouth of the Oswego River.
On May 5, the British fleet launched an attack that was repelled by the Americans. On the following day, an intensified assault featured heavy cannon fire from the British. Eventually, the Americans lost the fort and some important armaments, but most of the valuable supplies had been taken upriver to Oswego Falls (now Fulton) for safe storage. The preservation tactic worked, and shortly after the Battle of Oswego, a plan was in place to resume moving war supplies northward to the waiting ships at Sackets Harbor.
Following the attack, the British withdrew to Kingston, but a few weeks later, they were at the Galloo Islands near Sackets Harbor, blockading any marine attempts at supplying this strategic site. Should the materials slip through, it would dramatically tip the scales in favor of the American forces. By monitoring the harbor, the Brits were preventing that from happening, ensuring their superiority on the lake.
A British attempt to destroy the Superior was foiled, and on May 2, the ship was launched. But it was hardly battle-ready, still lacking guns and rigging. Less than three weeks after the attack on Oswego, the critical supplies hidden at Oswego Falls were once again on the move. They had already traveled from Brooklyn to Albany, and then to Oneida Lake. Now, from Oswego Falls, it was time for the final, dangerous leg of the journey.
A land contingent paralleled the 19 American boats as they fairly sneaked up the eastern shoreline of Lake Ontario. At Sandy Creek, the boats were taken inland as far as possible while scouts checked ahead for the presence of British ships. It was a wise move, for the enemy was indeed lurking nearby. Shortly after, the British launched an attack, but in less than a half hour, the Americans had won a resounding victory known as the Battle of Big Sandy Creek.
Despite the win, it was deemed unsafe to risk sending the valued supplies any farther by water, lest they again fall under attack and be captured or destroyed by the British. Wagons, oxen, horses, and manpower were summoned, both from the military and from local residents. The plan was to move the important supplies the remaining distance by land.
The bateaux (boats) were unloaded, and soon a lengthy caravan laden with guns, ship cables, and other supplies was on its way to Sackets Harbor, about 20 miles north. Only one item was yet to be moved—a length of rope, albeit an important one—and it presented a real problem.
This wasn't just any length of rope. It was intended as the anchor line and/or rigging for the USS Superior, the huge new frigate that could alter the balance of power on the lake. That meant this was a BIG rope. Most descriptions portrayed it as 6 inches thick and 600 feet long, weighing in at just under 5 tons.
No cart was big enough to handle its tremendous size and weight, but if it wasn't delivered, the Superior would remain port-bound, and the Brits would own the lake. Ingenuity often yields solutions at such critical moments, but sometimes good ol' elbow grease is the answer. In this case, it was a combination of the two, but the emphasis was clearly on the physical.
A section of the rope (referred to as a cable) was piled on a cart, and the remaining cable was strung out along the trail. Militiamen heaved it to their shoulders, and like one gigantic, ponderous snake, the cable began moving slowly northward behind the cart.
There are various accounts of the trip, and claims as to the number of cable-carriers range from 84 to more than 200. Some say that discouraged men skipped out of the nasty job after a few hours, and that locals stepped in, literally shouldering the burden. None of the stories differed on one count, though: participants were left badly bruised from the incredibly difficult ordeal.
But, they did it! The cable arrived at Sackets Harbor on the afternoon of the second day. The tired men wore abrasions, cuts, and huge, deep-purple bruises as hard-earned badges of valor. At the close of their incredible 20-mile journey, "there was loud cheering the whole length of the cable," as the men were greeted with music, drumming, flag-waving, and drink—and the princely sum of $2 each for their efforts.
They should have celebrated with a tug-of-war!
As soon as it was deemed seaworthy, the Superior turned the tables on the British, blockading their main shipyard at Kingston and helping establish American dominance of the lake. It was thanks in no small part to the "can-do" attitude exemplified by North Country pioneer folks.
Top Photo: Fort Ontario at Oswego.
Middle Photo: One of several plaques honoring the cable carriers.
Bottom Photo: Map of Lake Ontario sites.
Lawrence Gooley has authored ten books and dozens of articles on the North Country's past. He and his partner, Jill McKee, founded Bloated Toe Enterprises in 2004. Expanding their services in 2008, they have produced 19 titles to date, and are now offering web design. For information on book publishing, visit Bloated Toe Publishing.
Filed Under: Military History Tagged With: Canada, Lake Ontario, Lawrence Gooley, Maritime History, Oswego, Oswego County, Sackets Harbor, War of 1812
Hear Tales of Hauntings at The Farmers' Museum
October 21, 2010 by Editorial Staff Leave a Comment
During the most haunting time of the fall season, The Farmers' Museum invites visitors to experience "Things That Go Bump In The Night." Join museum interpreters as they lead you about the shadowy grounds and recount the many mysteries and ghostly happenings that have occurred within the buildings making up the Museum's historic village. These tours will be held on three nights only: Saturday, October 23; Friday, October 29; and Saturday, October 30, beginning at 5:30 p.m.
Museum guides will lead visitors through the darkened 19th-century village by lantern, stopping at various buildings throughout, including the Blacksmith's Shop and Bump Tavern, weaving ghostly tales adapted from the Louis C. Jones' classic, Things That Go Bump In the Night, a timeless record of haunted history and restless spirits in New York State. Participants will hear stories associated with the museum's buildings as in the tale of a young ghost sighted by staff and guests in Bump Tavern and the mysterious early morning strikes on the blacksmith's anvil.
These hour-long tours will be held every half-hour between 5:30 p.m. to 8:00 p.m. Reservations are required. Admission is $10 per person (ages 3 and up). Please call Meg Preston at (607) 547-1452.
Filed Under: Uncategorized Tagged With: Farmers' Museum, Oswego County
53rd Annual October Conference for Teachers
The 2010 October Conference for Teachers will present an evening performance by historical balladeer Linda Russell on Thursday, October 21 from 7:30 p.m. to 9:00 p.m. She will perform From Parlor and Porch: Music of 19th Century New York at The Farmers' Museum. This event is free and open to the public.
Ms. Russell's performance kicks off the 53rd Annual October Conference for Teachers being held October 21 & 22. The Conference is an annual professional development opportunity focused on current issues, topics, concerns, and practices in social studies education. Each year the Conference, a program sponsored by the New York State Historical Association, attracts several hundred educators to the campuses of Fenimore Art Museum and The Farmers' Museum during the fall season. This year, the Conference begins on Thursday evening, October 21, with a reception and Ms. Russell's performance, and continues on Friday, October 22, with a series or workshops and presentations offered by teachers and museum professionals.
Balladeer Linda Russell explores the music of 19th century New York through canal songs, lumberjack ballads, parlor tunes, minstrel melodies and hymns. With hammered and mountain dulcimers, guitar, pennywhistle and lumberjack, Ms. Russell illuminates the lives of the folks of the 1800's as seen in the popular songs that they sang.
Linda Russell is a historian, singer and actor who explores America's past through music. Having served for many years as a balladeer for the National Park Service at Federal Hall on Wall Street, the site of George Washington's inauguration, Ms. Russell takes her performances to historic sites, schools and festivals around the country. Appearances have included Lincoln Center-Out of Doors, the Metropolitan Museum of Art and the Carnegie Hall Folk Festival. She has recorded 8 albums of traditional American music.
The concert is free and open to the general public. For more information on the Conference or the evening performance, please call Tobi Voigt at (607) 547 1534. To see the full schedule of Conference events visit nysha.org.
Photo: Historical balladeer Linda Russell.
Filed Under: Conferences Tagged With: Education, Farmers' Museum, Oswego County