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Monitoring and strategic response to variants in severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) represent a considerable challenge in the current pandemic and for future viral outbreaks. Mutations/deletions of the virion’s prefusion Spike protein may have significant impact on vaccines and therapeutics that utilize this key structural protein in their mitigation strategies. In this study, we have demonstrated how dominant energetic landscape mappings (“glue points”) based on ab inito all-atom force fields coupled with phylogenetic sequence alignment information can identify key residue mutations and deletions associated with variants. We also found several examples of excellent homology of stabilizing residue glue points across the lineages of betacoronavirus Spike proteins that we have called “sequence homologous glue points.” SARS-CoV-2 demonstrates the least number of stabilizing glue points associated with interchain interactions among Down-state protomers across lineages. Additionally, we computationally studied variants among the trimeric Spike protein of SARS-CoV-2 using all-atom molecular dynamics to ascertain structural and energetic changes among variants. We examined both a theoretically based triple mutant and the UK or B.1.1.7 variant. For the theoretical triple mutant, we demonstrated through alanine substitutions that three key residues could cause the transition of Down-to-Up protomer states, where the transition is characterized by the “arm” length of the receptor-binding domain (RBD) rather than the hinge angle. For the B.1.1.7 variant, we demonstrated the critical importance of mutations D614G and N501Y on the structure and binding, respectively, of the Spike protein. We note that these same two key mutations are also found in the South African B.1.351 variant. IMPORTANCE Viral variants represent a major challenge to monitoring viral outbreaks and formulating strategic health care responses. Variants represent transmitting viruses that have specific mutations and deletions associated with their genome. In the case of SARS-CoV-2 and other related viruses (betacoronaviruses), many of these mutations and deletions are associated with the Spike protein that the virus uses to infect cells. Here, we have analyzed both SARS-CoV-2 variants and related viruses, such as Middle Eastern respiratory syndrome coronavirus (MERS-CoV), in order to understand not only differences, but also key similarities between them. Understanding similarities can be as important as differences in determining key functional features of a class of viruses, such as the betacoronaviruses. We have used both phylogenetic analysis, which traces genetic similarities and differences, along with independent biophysics analysis, which adds function or behavior, in order to determine possible functional differences and hence possible transmission and infection differences among variants and lineages.

Monitoring and strategic response to variants in SARS-CoV-2 represents a considerable challenge in the current pandemic, as well as potentially future viral outbreaks of similar magnitude. In particular mutations and deletions involving the virion’s prefusion Spike protein have significant potential impact on vaccines and therapeutics that utilize this key structural viral protein in their mitigation strategies. In this study, we have demonstrated how dominant energetic landscape mappings (“glue points”) coupled with sequence alignment information can potentially identify or flag key residue mutations and deletions associated with variants. Surprisingly, we also found excellent homology of stabilizing residue glue points across the lineage of β coronavirus Spike proteins, and we have termed this as “sequence homologous glue points”. In general, these flagged residue mutations and/or deletions are then computationally studied in detail using all-atom biocomputational molecular dynamics over approximately one microsecond in order to ascertain structural and energetic changes in the Spike protein associated variants. Specifically, we examined both a theoretically-based triple mutant and the so-called UK or B.1.1.7 variant. For the theoretical triple mutant, we demonstrated through Alanine mutations, which help “unglue” key residue-residue interactions, that these three key stabilizing residues could cause the transition of Down to Up protomer states, where the Up protomer state allows binding of the prefusion Spike protein to hACE2 host cell receptors, whereas the Down state is believed inaccessible. Thus, we are able to demonstrate the importance of glue point residue identification in the overall stability of the prefusion Spike protein. For the B.1.1.7 variant, we demonstrated the critical importance of D614G and N5017 on the structure and binding, respectively, of the Spike protein. Notably, we had previously identified D614 as a key glue point in the inter-protomer stabilization of the Spike protein prior to the emergence of its mutation. The mutant D614G is a structure breaking Glycine mutation demonstrating a relatively more distal Down state RBD and a more stable conformation in general. In addition, we demonstrate that the mutation N501Y may significantly increase the Spike protein binding to hACE2 cell receptors through its interaction with Y41 of hACE2 forming a potentially strong hydrophobic residue binding pair. We note that these two key mutations, D614G and N501Y, are also found in the so-called South African (SA; B.1.351) variant of SARS-CoV-2. Future studies along these lines are, therefore, aimed at mapping glue points to residue mutations and deletions of associated prefusion Spike protein variants in order to help identify and analyze possible “variants of interest” and optimize efforts aimed at the mitigation of this current and future virions.

A 2500-year history of invasion, conquest, and resistance has left Afghanistan ethnically diverse and culturally rich. And yet, this storied history has bequeathed to the nation’s people a legacy of political fragmentation, economic impoverishment, and in recent times, even some international isolation. The last 40 years of relentless conflict, encompassing two superpower invasions and decades of a smoldering civil war, have placed entire generations of Afghans at risk for posttraumatic stress disorder and have pushed the nation into a cycle of poverty, reduced educational opportunity, and violence. It is the contention of this paper that several academic concepts–the neuroscience principle of propinquity, the scholarly disciplines of behavioral economics and game theory, and the blockchain technology promoted by “Satoshi Nakamoto”—can be woven together into a practical application to create business partnerships, jobs, and an entrepreneurial middle class for Afghanistan, thereby decreasing poverty and the fallout of crime and violence significantly. Based on these principles, a genuinely non-exploitative partnership structure can be built between United States and Afghan interests. The central role of military can be replaced by private sector players, to achieve through human security what could not be achieved through kinetic force. In such a diverse culture, and amidst the difficulties of Afghanistan’s geographical and topographical scenario, military dominance in Afghanistan has always failed, for thousands of years. Yet, that never would have been the true solution anyway. It seldom is. Afghanistan may utilize its vast mineral wealth as a starting place for trade, human security and national security, assisted but unexploited. And done in partnerships rather than as suppliers, they may then begin to extract the wealth of its human resources and find its future as a contributing and secure world citizen. The discussion below will sketch a broad outline of a possible path forward, employing twenty-first century innovative business structure to solve for the underlying long-standing impediments to security and prosperity. Like gravity, applications of these principles are true whenever humans compete for value or security. Anywhere self-interests have vetoed the common good, to the ultimate demise of both, these principles and guidelines that follow will prove useful for building the hope of a nation.

The SARS-CoV-2 virion responsible for the current world-wide pandemic COVID-19 has a characteristic Spike protein (S) on its surface that embellishes both a prefusion state and fusion state. The prefusion Spike protein (S) is a large trimeric protein where each protomer may be in a so-called Up state or Down state, depending on the configuration of its receptor binding domain (RBD) within its distal, prefusion S1 domain. The Up state is believed to allow binding of the virion to ACE-2 receptors on human epithelial cells, whereas the Down state is believed to be relatively inactive or reduced in its binding behavior. We have performed detailed all-atom, dominant energy landscape mappings for noncovalent interactions (charge, partial charge, and van der Waals) of the SARS-CoV-2 Spike protein in its static prefusion state based on two recent and independent experimental structure publications. We included both interchain interactions and intrachain (domain) interactions in our mappings in order to determine any telling differences (different so-called “glue” points) between residues in the Up and Down state protomers. The S2 proximal, fusion domain demonstrated no appreciable energetic differences between Up and Down protomers, including interchain as well as each protomer’s intrachain, S1-S2 interactions. However, the S1 domain interactions across neighboring protomers, which include the RBD-NTD cross chain interactions, showed significant energetic differences between Up-Down and Down-Down neighboring protomers. This included, for example, a key RBD residue ARG357 in the Up-Down interaction and a three residue sequence ALA520-PRO521-ALA522, associated with a turn structure in the RBD of the Up state protomer, acting as a stabilizing interaction with the NTD of its neighbor protomer. Additionally, our intra chain dominant energy mappings within each protomer, identified a significant “glue” point or possible “latch” for the Down state protomer between the S1 subdomain, SD1, and the RBD domain of the same protomer that was completely missing in the Up state protomer analysis. Ironically, this dominant energetic interaction in the Down state protomer involved the backbone atoms of the same three residue sequence ALA520-PRO521-ALA522 of the RBD with the amino acid R-group of GLN564 in the SD1 domain. Thus, this same three residue sequence acts as a stabilizer of the RBD in the Up conformation through its interactions with its neighboring NTD chain and a kind of latch in the Down state conformation through its interactions with its own SD1 domain. The dominant interaction energy residues identified here are also conserved across reported variations of SARS-CoV-2, as well as the closely related virions SARS-Cov and the bat corona virus RatG13. We conducted preliminary molecular dynamics simulations across 0.1 μ seconds to see if this latch provided structural stability and indeed found that a single point mutation (Q564G) resulted in the latch releasing transforming the protomer from the Down to the Up state conformation. Full trimeric Spike protein studies of the same mutation across all protomers, however, did not exhibit latch release demonstrating the critical importance of interchain interactions across the S1 domain, including RBD-NTD neighboring chain interactions. Therapies aimed at disrupting these noncovalent interactions could be a viable route for the physico-chemical mitigation of this deadly virion.

The SARS-Cov-2 virion responsible for the current world-wide pandemic Covid-19 has a characteristic Spike protein (S) on its surface that embellishes both a prefusion state and fusion state. The prefusion Spike protein (S) is a large trimeric protein where each protomer may be in a so-called Up state or Down state, depending on the configuration of its receptor binding domain (RBD). The Up state is believed to allow binding of the virion to ACE-2 receptors on human epithelial cells, whereas the Down state is believed to be relatively inactive or reduced in its binding behavior. We have performed detailed all-atom, dominant energy landscape mappings for noncovalent interactions (charge, partial charge, and van der Waals) of the SARS-Cov-2 Spike protein in its static prefusion state based on recent structural information. We included both interchain interactions and intrachain (domain) interactions in our mappings in order to determine any telling differences (different so-called “glue” points) between residues in the Up and Down state protomers. In general, the S2 or fusion machinery domain of S is relatively rigid with strong noncovalent interactions facilitated by helical secondary structures, whereas the S1 domain, which contains the RBD and N-terminal domain (NTD), is relatively more flexible and characterized by beta strand structural motifs. The S2 domain demonstrated no appreciable energetic differences between Up and Down protomers, including interchain as well as each protomer’s intrachain, S1-S2 interactions. However, the S1 domain interactions across neighboring protomers, which include the RBD-NTD cross chain interactions, showed significant energetic differences between Up-Down and Down-Down neighboring protomers. Surprisingly, the Up-Down, RBD-NTD interactions were overall stronger and more numerous than the Down-Down cross chain interactions, including the appearance of the three residue sequence ALA520-PRO521-ALA522 associated with a turn structure in the RBD of the Up state protomer. Additionally, our intrachain dominant energy mappings within each protomer, identified a significant “glue” point or possible “latch” for the Down state protomer between the S1 subdomain, SD1, and the RBD domain of the same protomer that was completely missing in the Up state protomer analysis. Ironically, this dominant energetic interaction in the Down state protomer involved the backbone atoms of the same three residue sequence ALA520-PRO521-ALA522 of the RBD with the R-group of GLN564 in the SD1 domain. Thus, this same three residue sequence acts as a stabilizer of the RBD in the Up conformation through its interactions with its neighboring NTD chain and a kind of latch in the Down state conformation through its interactions with its own SD1 domain. The dominant interaction energy residues identified here are also conserved across reported variations of SARS-Cov-2, as well as the closely related virions SARS-Cov and the bat corona virus RatG13. To help verify the potential latch for the Down state protomer, we conducted some preliminary molecular dynamic simulations that effectively turn off this specific latch glue point via a single point mutation of GLN564. Interestingly, the single point mutation lead to the latch releasing in less than a few nanoseconds, but the latch remained fixed in the wild state protomer for up to 0.1 microseconds that were simulated. Many more detailed studies are needed to understand the dynamics of the Up and Down states of the Spike protein, including the stabilizing chain-chain interactions and the mechanisms of transition from Down to Up state protomers. Nonetheless, static dominant energy landscape mappings and preliminary molecular dynamic studies given here may represent a useful starting point for more detailed dynamic analyses and hopefully an improved understanding of the structure-function relationship of this highly complex protein associated with COVID-19.

The 793nm semiconductor diode cladding pumped Thulium-doped high power fiber laser operates around eye safe 1.9 ~ 2μm and output power can reach to kW level. Those 2μm high power fiber lasers are attractive in various applications in industrial use, medical field, remote sensing and military use. High power, reliable 793nm diodes and cost-effective pump modules are the key component in enabling widespread use of Tm-doped 2μm fiber laser for commercial applications. The latest generation of Coherent AAATM epi design platform is optimized for low internal loss, high quantum efficiency and higher linear power density at 793nm region. Two types of high power diode lasers are tested; one is a single emitter with 100μm emission width and the other is a tailored bar (T-bar) including five 100μm emitters with 1mm pitch. The single emitter can achieve 5.6W output power at 5A with 1.26W/A slope efficiency and 60.3% E/O efficiency. Those single emitters are packaged and coupled into a 100μm fiber. At 5A current, a three single emitter based 100μm fiber-coupled module’s output power is 13.4W and the E/O efficiency is 48.0%. The T-bar can reach up to 30W output power at 30A with 1.19W/A slope efficiency and 56.4% peak E/O efficiency. Nine T-bars are mounted and coupled into a 225μm fiber-coupled module and 150W output power and 47.3% E/O efficiency are achieved at 19.1A current. Both single emitter based and T-bar based fiber-coupled modules show long reliable life; single emitters based module’s life is more than 20,000 h at 4A and T-bars based module’s life is more than 10,000 h at 20A.

In this article, a black-box higher order fast multipole method for solving boundary integral equations on parametric surfaces in three spatial dimensions is proposed. Such piecewise smooth surfaces are the topic of recent studies in isogeometric analysis. Due to the exact surface representation, the rate of convergence of higher order methods is not limited by approximation errors of the surface. An element-wise clustering strategy yields a balanced cluster tree and an efficient numerical integration scheme for the underlying Galerkin method. By performing the interpolation for the fast multipole method directly on the reference domain, the cost complexity in the polynomial degree is reduced by one order. This gain is independent of the application of either (mathcal{H})- or (mathcal{H}^2)-matrices. In fact, several simplifications in the construction of (mathcal{H}^2)-matrices are pointed out, which are a by-product of the surface representation. Extensive numerical examples are provided in order to quantify and qualify the proposed method. In this article, a black-box higher order fast multipole method for solving boundary integral equations on parametric surfaces in three spatial dimensions is proposed. Such piecewise smooth surfaces are the topic of recent studies in isogeometric analysis. Due to the exact surface representation, the rate of convergence of higher order methods is not limited by approximation errors of the surface. An element-wise clustering strategy yields a balanced cluster tree and an efficient numerical integration scheme for the underlying Galerkin method. By performing the interpolation for the fast multipole method directly on the reference domain, the cost complexity in the polynomial degree is reducedby one order. This gain is independent of the application of either H - or H 2- matrices. In fact, several simplificationsin the construction of H 2 -matrices are pointed out, which are a by-product of the surface representation. Extensive numerical examples are provided in order to quantify and qualify the proposed method.

This article is dedicated to the rapid computation of separable expansions for the approximation of random fields. We consider approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. Especially, we provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms of the trace. Numerical examples are provided to validate and quantify the presented methods.

This article is dedicated to the anisotropic sparse grid quadrature for functions which are analytically extendable into an anisotropic tensor product domain. Taking into account this anisotropy, we end up with a dimension independent error versus cost estimate of the proposed quadrature. In addition, we provide a novel and improved estimate for the cardinality of the underlying anisotropic index set. To validate the theoretical findings, we present several examples ranging from simple quadrature problems to diffusion problems on random domains. These examples demonstrate the remarkable convergence behavior of the anisotropic sparse grid quadrature in applications.

We consider the efficient solution of partial differential equations for strongly elliptic operators with constant coefficients and stochastic Dirichlet data by the boundary integral equation method. The computation of the solution's two-point correlation is well understood if the two-point correlation of the Dirichlet data is known and sufficiently smooth. Unfortunately, the problem becomes much more involved in case of roughly correlated data. We will show that the concept of the $${\mathcal {H}}$$ H -matrix arithmetic provides a powerful tool to cope with this problem. By employing a parametric surface representation, we end up with an $${\mathcal {H}}$$ H -matrix arithmetic based on balanced cluster trees. This considerably simplifies the implementation and improves the performance of the $${\mathcal {H}}$$ H -matrix arithmetic. Numerical experiments are provided to validate and quantify the presented methods and algorithms.

The present article is concerned with solving Bernoulli’s exterior free boundary problem in case of an interior boundary which is random. We model this random free boundary problem such that the expectation and the variance of the sought domain can be defined. In order to numerically approximate the expectation and the variance, we propose a sampling method like the (quasi-) Monte Carlo quadrature. The free boundary is determined for each sample by the trial method which is a fixed-point like iteration. Extensive numerical results are given in order to illustrate the model.

We present recent development of single lateral mode 1050 nm laser bars. The devices are based on an InGaAs/AlGaAs single quantum well and an asymmetric large optical cavity waveguide structure. By optimizing the AlGaAs composition, doping profiles, and QW thickness, the low internal loss of 0.5 cm-1 and high internal quantum efficiency of 98% are obtained. A standard bar (10% fill factor; 4mm cavity length) reaches 72% peak electro-optical efficiency and 1.0 W/A slope efficiency at 25°C. To achieve high single lateral mode power, the current confinement and optical loss profile in lateral direction are carefully designed and optimized to suppress higher order lateral modes. We demonstrate 1.5W single lateral mode power per emitter from a 19-emitter 10mm bar at 25°C. High electro-optical efficiency are also demonstrated at 25°C from two separate full-bar geometries on conduction cooled packaging: 20 W with

SummaryAs you increase the dimension of a sphere with fixed radius into the realm of hypergeometry, the volume increases—for a while. We explore the counterintuitive result that, as we keep adding dimensions, eventually the volume decreases.

We consider the efficient deterministic solution of elliptic boundary value problems with random diffusion matrix. Assuming random perturbations with known k moments, we derive, to leading order in the random perturbation?s amplitude, deterministic equations for k moments of the random solution. The solution?s k-th moment satisfies a k-fold tensor product boundary value problem on the k-fold product domain which can efficiently be discretized in sparse tensor product spaces. By defining the complement spaces via Galerkin projections, the related system of linear equations decouples and can be solved by standard multilevel finite element solvers. Numerical results for k = 2 are presented to validate and quantify our theoretical findings.

We compare fast black-box boundary element methods on parametric surfaces in $\mathbb{R}^3$. These are the adaptive cross approximation, the multipole method based on interpolation, and the wavelet Galerkin scheme. The surface representation by a piecewise smooth parameterization is in contrast to the common approximation of surfaces by panels. Nonetheless, parametric surface representations are easily accessible from Computer Aided Design (CAD) and are recently topic of the studies in isogeometric analysis. Especially, we can apply two-dimensional interpolation in the multipole method. A main feature of this approach is that the cluster bases and the respective moment matrices are independent of the geometry. This results in a superior compression of the far field compared to other cluster methods.

This article is dedicated to the computation of the moments of the solution to elliptic partial differential equations with random, log-normally distributed diffusion coefficients by the quasi-Monte Carlo method. Our main result is that the convergence rate of the quasi-Monte Carlo method based on the Halton sequence for the moment computation depends only linearly on the dimensionality of the stochastic input parameters. Especially, we attain this rather mild dependence on the stochastic dimensionality without any randomization of the quasi-Monte Carlo method under consideration. For the proof of the main result, we require related regularity estimates for the solution and its powers. These estimates are also provided here. Numerical experiments are given to validate the theoretical findings. This article is dedicated to the computation of the moments of the solution to elliptic partial differential equations with random, log-normally distributed diffusion coefficients by the quasi-Monte Carlo method. Our main result is that the convergence rate of the quasi-Monte Carlo method based on the Halton sequence for the moment computation depends only linearly on the dimensionality of the stochastic input parameters. Especially, we attain this rather mild dependence on the stochastic dimensionality without any randomization of the quasi-Monte Carlo method under consideration. For the proof of the main result, we require related regularity estimates for the solution and its powers. These estimates are also provided here. Numerical experiments are given to validate the theoretical findings.

The pathology of Alzheimer’s disease can ultimately be traced to the increased aggregation stability of Aβ42 peptides which possess two extra residues (Ile 41 & Ala 42) that the non-pathological strain (Aβ40) lacks. We have found Aβ42 fibrils to exhibit stronger energies in inter-chain interactions and we have also identified the cause for this increase to be the result of different Ramachandran angle values in certain residues of the Aβ42 strain compared to Aβ40. These unique angle configurations result in the peptide planes in the fibril structures to be more vertical along the fibril axis for Aβ42 which thus reduces the inter-atomic distance between interacting atoms on vicinal peptide chains thereby increasing the electrostatic interaction energies. We lastly postulate that these different Ramachandran angle values could possibly be traced to the unique conformational folding avenues sampled by the Aβ42 peptide owing to the presence of its two extra residues.

We report on our progress developing long wavelength high power laser diodes based on the InGaAsP/InP alloy system emitting in the range from 1400 to 2010 nm. Output power levels exceeding 50 Watts CW and 40% conversion efficiency were obtained at 1470 nm wavelength from 20% fill factor (FF) bars with 2 mm cavity length mounted on water cooled plates. Using these stackable plates we built a water cooled stack with 8 bars, successfully demonstrating 400 W at 1470 nm with good reliability. In all cases the maximum conversion efficiency was greater than 40% and the maximum power achievable was limited by thermal rollover. For lasers emitting in the range from 1930 to 2010 nm we achieved output power levels over 15 W and 20 % conversion efficiency from 20% FF bars with 2 mm cavity length on a conductively cooled platform. Life testing of the 1470 nm lasers bars over 14,000 hours under constant current mode has shown no significant degradation.

The present paper is dedicated to the application of the pivoted Cholesky decomposition to compute low-rank approximations of dense, positive semi-definite matrices. The resulting truncation error is rigorously controlled in terms of the trace norm. Exponential convergence rates are proved under the assumption that the eigenvalues of the matrix under consideration exhibit a sufficiently fast exponential decay. By numerical experiments it is demonstrated that the pivoted Cholesky decomposition leads to very efficient algorithms to separate the variables of bi-variate functions.

Following Irving and Kirkwood’s (J. Chem. Phys. 1950, 18, 817) classical approach to the statistical mechanics of transport processes and the conservation equations for mass, momentum, and energy, we introduce a particular dynamical variable for entropy and derive the general nonequilibrium entropy conservation equation. This particular formalism is shown to encompass both Boltzmann’s and Gibbs’ entropy definitions as special cases. Entropy generation is shown to follow from phase-space dimensionality loss and truncations or approximations in higher-order space, the latter of which is consistent with the thesis of Jaynes (Am. J. Phys. 1965, 33, 391). The general approach to entropy conservation given here not only completes Irving and Kirkwood’s treatment of the transport equations but also allows for a consistent analysis of all transport equations for any given system. Following standard perturbation expansion methods about local equilibrium states, we derive the closed form of the entropy conservation ...

Introduction: HIV viral envelope proteins are targets for small inhibitor molecules aimed at disrupting the cellular entry process. Potential peptide-class inhibitor molecules (rDNA drugs) have been previously identified, with mixed results, through biomimicry and phage display experimental methods. Here we describe a new approach based on computational fragment discovery. The method has the potential to not only optimize peptide binding affinity but also to rapidly produce alternative inhibitors against mutated strains. Methods: A comprehensive, all-atom implicit solvent method is used to bombard the C-heptad repeat unit of HIV-1 target envelope protein GP41 with single Damino acid residues as they exist in their native state. A nascent peptide computational search process then identifies potential favorable sequences of attached ligands based on four peptide bond criteria. Finally, dynamic simulations of nascent peptides attached to host targets help refine potential peptide inhibitors for experimental HIV-1 challenge assays and testing. Results and Discussion: Initial testing of the method was done using 64,000 total ligands of D-amino acid residues at a total computational time of 0.05 microseconds per ligand, which resulted in several thousand attached ligands. Peptide bond criteria search employing three of the four bond constraints with a tolerance of 20 percent, resulted in four potential peptide inhibitors of 5 to 6 residues in length. Only one of the four peptides demonstrated IC50 values and partial viral inhibition based on cell challenge assays using CEM-SS host cells. That peptide inhibitor also computationally demonstrated longtime attachment and stability to a helical groove in its C-heptad target. This initial testing of peptide fragment discovery against HIV-1 has helped us refine the protocols and identify key areas of improvement. Conclusion: Our methods demonstrate the potential to design efficient peptide inhibitors to viral target proteins based on an all-atom dynamic simulation and using a ligand library as fragments of potential nascent peptides. Our methods can be greatly improved through the use of higher numbers of ligands, increased time of bombardment, and tighter constraints on the peptide bond search step. Our method may be important in the need to rapidly respond to target mutations and to advance multiple targeting methods based multiple peptide inhibitors.

In this article, we propose the sparse grid combination technique for the second moment analysis of elliptic partial differential equations on random domains. By employing shape sensitivity analysis, we linearize the influence of the random domain perturbation on the solution. We derive deterministic partial differential equations to approximate the random solution’s mean and its covariance with leading order in the amplitude of the random domain perturbation. The partial differential equation for the covariance is a tensor product Dirichlet problem which can efficiently be determined by Galerkin's method in the sparse tensor product space. We show that this Galerkin approximation coincides with the solution derived from the combination technique provided that the detail spaces in the related multiscale hierarchy are constructed with respect to Galerkin projections. This means that the combination technique does not impose an additional error in our construction. Numerical experiments quantify and qualify the proposed method.

In this article, we provide a rigorous analysis of the solution to elliptic diffusion problems on random domains. In particular, based on the decay of the Karhunen-Lo`eve expansion of the domain perturbation field, we establish decay rates for the derivatives of the random solution that are independent of the stochastic dimension. For the implementation of a related approximation scheme, like quasi-Monte Carlo quadrature, stochastic collocation, etc., we propose parametric finite elements to compute the solution of the diffusion problem on each individual realization of the domain generated by the perturbation field. This simplifies the implementation and yields a non-intrusive approach. Having this machinery at hand, we can easily transfer it to stochastic interface problems. The theoretical findings are complemented by numerical examples for both, stochastic interface problems and boundary value problems on random domains. In this article, we provide a rigorous analysis of the solution to elliptic diffusion problems on random domains. In particular, based on the decay of the Karhunen-Loeve expansion of the domain perturbation field, we establish decay rates for the derivativesof the random solution that are independent of the stochastic dimension. For the implementation of a related approximation scheme, like quasi-Monte Carlo quadrature, stochastic collocation, etc., we propose parametric finite elements to compute the solution of the diffusion problem on each individual realization of the domain generated by the perturbation field. This simplifies the implementation and yields a non-intrusive approach. Having this machinery at hand, we can easily transfer it to stochastic interface problems. The theoretical findings are complemented by numerical examples for both, stochastic interface problems and boundary value problems on random domains.

This article is dedicated to multilevel quadrature methods for the rapid solution of stochastic partial differential equations with a log-normally distributed diffusion coefficient. The key idea of such approaches is a sparse-grid approximation of the occurring product space between the stochastic and the spatial variable. We develop the mathematical theory and present error estimates for the computation of the solution's moments with focus on the mean and the variance. Especially, the present framework covers the multilevel Monte Carlo method and the multilevel quasi-Monte Carlo method as special cases. The theoretical findings are supplemented by numerical experiments. This article is dedicated to multilevel quadrature methods forthe rapid solution of stochastic partial differential equationswith a log-normally distributed diffusion coefficient. The key ideaof such approaches is a sparse-grid approximation of the occurring product space between the stochastic and the spatial variable. We develop the mathematical theory and present error estimates for the computation of the solution's moments with focus on the mean and the variance. Especially, the present framework covers the multilevel Monte Carlo method and the multilevel quasi-Monte Carlo method as special cases. The theoretical findings are supplemented by numerical experiments.

ACL; International audience; This article is dedicated to the solution of Bernoulli's exterior free boundary problem in the situation of a random interior boundary. We provide the theoretical background that ensures the well-posedness of the problem under consideration and describe two different frameworks to define the expectation and the deviation of the resulting annular domain. The first approach is based on the Vorob'ev expectation, which can be defined for arbitrary sets. The second approach is based on the particular parametrization. In order to compare these approaches, we present analytical examples for the case of a circular interior boundary. Additionally, numerical experiments are performed for more general geometric configurations. For the numerical approximation of the expectation and the deviation, we propose a sampling method like the Monte Carlo or the quasi-Monte Carlo quadrature. Each particular realization of the free boundary is then computed by the trial method, which is a fixed-point-like iteration for the solution of Bernoulli's free boundary problem.

This article reports on the use of the House of Quality to facilitate the design of a required operations management course in an MBA program. The House of Quality is a relatively new approach that is used in product or service design and total quality management. The faculty identified the decision issues it felt would be pertinent to the design effort and surveyed students on their perceptions of those areas at the end of the course. The faculty then analyzed data and discussed the findings. The resulting House of Quality provided the basis for determining future course improvements.

For certain processes, the quality of the output can be monitored using attribute inspection statistical process control. Various approaches have been used to determine optimal or near-optimal parameters for such a plan. Since most of these approaches use an unconstrained model, some solutions can result in theoretical and pragmatic problems. In this paper we used Duncan's loss function as the objective function for the development of a Genetic Algorithm (GA). In addition to formulating a GA to find a solution to the model, user constraints concerning the frequency of inspection, the number of defects allowed and the production rate are used to limit the search space for the GA. The GA is selected over other search techniques such as traditional calculus-based, enumeration, or undirected random search methods because the GA is more robust than other search techniques.

Predicting the long-time, nonequi- librium dynamics of receptor-ligand interactions for structured proteins in a host fluid is a formi- dable task, but of great importance to predicting and analyzing cell-signaling processes and small molecule drug efficacies. Such processes take place on timescales on the order of milliseconds to sec- onds, so "brute-force" real-time, molecular or atomic simulations to determine absolute ligand-binding rates to receptor targets and over a statistical en- semble of systems are not currently feasible. In the current study, we implement on real protein sys- tems a previously developed 3-5 hybrid molecular dynamics/Brownian dynamics algorithm, which takes advantage of the underlying, disparate time- scales involved and overcomes the limitations of brute-force approaches. The algorithm is based on a multiple timescale analysis of the total system Ham- iltonian, including all atomic and molecular struc- ture information for the system: water, ligand, and receptor. In general, the method can account for the complex hydrodynamic, translational-orientational diffusion aspects of ligand-docking dynamics as well as predict the actual or absolute rates of ligand binding. To test some of the underlying features of the method, simulations were conducted here for an artificially constructed spherical protein "made" from the real protein insulin. Excellent compari- sons of simulation calculations of the so-called grand particle friction tensor to analytical values were obtained for this system when protein charge ef- fects were neglected. When protein charges were included, we found anomalous results caused by the alteration of the spatial, microscopic structure of water proximal to the protein surface. Protein charge effects were found to be highly significant and consistent with the recent hypothesis of Hop- pert and Mayer (Am Sci 1999;87:518 -525) for charged macromolecules in water, which involves the forma- tion of a "water dense region" proximal to the charged protein surface followed by a "dilute water region." We further studied the algorithm on a D-peptide/HIV capside protein system and demon- strated the algorithms utility to study the nonequi- librium docking dynamics in this contemporary problem. In general, protein charge effects, which alter water structural properties in an anomalous fashion proximal to the protein surface, were found to be much more important than the so-called hydro- dynamic interaction effects between ligand and re- ceptor. The diminished role of hydrodynamic inter- actions in protein systems allows for a much simpler overall dynamic algorithm for the nonequilibrium protein-docking process. Further studies are now underway to critically examine this simpler overall algorithm in analyzing the nonequilibrium protein- docking problem. Proteins 2003;52:339 -348.

In this study, the authors investigated the efficacy of requiring graded homework problems in an introductory operations management course. Using grades on multiple-choice tests as the performance measure, the authors tested hypotheses concerning the effect of requiring graded homework on the exam performance of 330 students. Results indicate that requiring graded homework had a negative effect on exam performance.

Business‐to‐business (B2B) e‐commerce activity provides many growth opportunities for firms willing to explore this new approach. While B2B is often considered the domain of larger firms, the potential benefits of access to new clients, access to new global markets, and product line expansion are of particular importance to entrepreneurial suppliers. This article examines these benefits, as well as various mistakes an entrepreneurial firm may make in pursuing B2B e‐commerce. From this discussion, we recommend five action steps a firm should take to reap the tremendous benefits of supplying through a B2B network.

Beginning with the molecular-based Fokker–Planck equation obtained previously [M. H. Peters, J. Chem. Phys. 110, 528 (1999); J. Stat. Phys. 94, 557 (1999)], the Smoluchowski diffusion equation is derived here to describe the spatial and orientational dynamics of molecularly structured macromolecules near molecularly structured surfaces. The formal scaling and perturbation methods employed allow the establishment of definite limits on the use of the Smoluchowski equation when surfaces are present. It is shown that the Smoluchowski equation reduces to that given previously [D. W. Condiff and J. S. Dahler, J. Chem. Phys. 44, 3988 (1966)] in the absence of external surfaces. A specific example application is given involving a spherical macromolecule with electrostatic charge segments near a planar surface with an arbitrary charge distribution. Finally, we show that the short-time solution to the Smoluchowski equation obtained here yields a Brownian dynamics method consistent with that given previously [E. Dickinson, S. A. Allison, and J. A. McCammon, J. Chem. Soc. Faraday Trans. 2 81, 591 (1985)] for orientable, interacting Brownian particles. This study has applications to problems involving site-specific adsorption of orientable, structured Brownian particles, such as association or adsorption of biological macromolecules to cellular surfaces and enzyme–substrate docking kinetics, to name a few.

The Fokker-Planck equation and molecular-based grand friction tensor are derived for the problem of rotational and translational motions of a structured Brownian particle, including the presence of a structured wall. Using the method of multiple time scales, it is shown that the time independent, grand friction tensor for the Brownian particle includes, in a general way, terms that account for the fluid molecular mediated interactions with the wall. The resulting Fokker-Planck equation has important applications in processes involving site-specific adsorption of macromolecules, such as affinity chromotography, biological separations, and numerous cellular processes involving attachment of macromolecules.

A simple, static contact mapping algorithm has been developed as a first step at identifying potential peptide biomimetics from protein interaction partner structure files. This rapid and simple mapping algorithm, “OpenContact” provides screened or parsed protein interaction files based on specified criteria for interatomic separation distances and interatomic potential interactions. The algorithm, which uses all-atom Amber03 force field models, was blindly tested on several unrelated cases from the literature where potential peptide mimetics have been experimentally developed to varying degrees of success. In all cases, the screening algorithm efficiently predicted proposed or potential peptide biomimetics, or close variations thereof, and provided complete atom-atom interaction data necessary for further detailed analysis and drug development. In addition, we used the static parsing/mapping method to develop a peptide mimetic to the cancer protein target, epidermal growth factor receptor. In this case, secondary, loop structure for the peptide was indicated from the intra-protein mapping, and the peptide was subsequently synthesized and shown to exhibit successful binding to the target protein. The case studies, which all involved experimental peptide drug advancement, illustrate many of the challenges associated with the development of peptide biomimetics, in general. Proteins 2014; 82:2253–2262. © 2014 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.

In this study, the grand (translational) friction tensor for free‐molecule (large Knudsen number) flows over two, unequal‐size cylinders is obtained analytically considering both ‘‘shielding’’ effects and multiple collisions off cylinder surfaces, as well as including both diffuse and specular molecule‐surface boundary conditions. A perturbation solution is used where the leading‐order term accounts for molecular collisions from the free‐streaming gas including all shielding effects. The first‐order correction term is also obtained here and accounts for collisions by molecules reflected off neighboring surfaces from the free‐stream gas. It is shown that the grand friction tensor is symmetric under the conditions of small ratios of the free‐stream gas velocity to the thermal gas velocity, the same type of molecular reflection boundary condition on both cylinders, and constant temperature. It is also shown that the two‐term expansion formula is accurate under isothermal conditions in the so‐called ‘‘far‐fie...

Decisions relating to adoption and use of just‐in‐time (JIT) are typically based on economic considerations. Experience with JIT systems indicates that certain non‐economic issues can arise which affect long‐term profitability. Suggests that stakeholder theory be used to consider JIT from a realistic and complete perspective. According to stakeholder theory, there are shared interests or interdependence between organizations and the various groups that have a stake in the firm. Thus organizations must consider their social responsibilities to their stakeholders, namely, economic, legal, ethical and philanthropic responsibilities. Discusses certain aspects of JIT that can generate ethical and philanthropic concerns related to a firm′s principal stakeholders – employers, suppliers, community, owners and customer. Concludes with a list of questions to initiate the process of identifying these types of issues for each stakeholder group.

A two-stage screening procedure is developed for a situation where an item is sold in one of two markets or scrapped. The item's selling price and product specifications are different in both markets. In the first stage of the procedure, each item is inspected on a surrogate variable that is correlated with the perfornance variable of interest. If a decision is not reached at this point, the item is subjected to the second-stage of the procedure where it is inspected on the performance variable, and a classification decision is made. A loss in revenue is incurred by the producer when an item that meets the specifications of the higher-price market is sold in the lower-price market. The producer also sustains a cost when an item that does not conform to the product specifications of a market is sold in that market. The economic factors considered in the model, therefore, are the selling prices and the cost consequences resulting from decision errors. The optimal screening specification limits for known-parameter and unknown-parameters situations are derived by maximizing the expected profit per item.

The transport of flexible biological macromolecules in confined geometries is found in a variety of important biophysical systems including biomolecular movements through pores in cell walls, vesicle walls, and synthetic nanopores for sequencing methods. In this study, we extend our previous analysis of the Fokker-Planck and Langevin dynamics for describing the coupled translational and rotational motions of single structured macromolecules near structured external surfaces or walls [M. H. Peters, J. Chem. Phys. 110, 528 (1999); 112, 5488 (2000)] to the problem of many interacting macromolecules in the presence of structured external surfaces representing the confining geometry. Overall macromolecular flexibility is modeled through specified interaction potentials between the structured Brownian subunits (B-particles), as already demonstrated for protein and DNA molecules briefly reviewed here. We derive the Fokker-Planck equation using a formal multiple time scale perturbation expansion of the Liouville equation for the entire system, i.e., solvent, macromolecules, and external surface. A configurational-orientational Langevin displacement equation is also obtained for use in Brownian dynamics applications. We demonstrate important effects of the external surface on implicit solvent forces through formal descriptions of the grand friction tensor and equilibrium average force of the solvent on the B-particles. The formal analysis provides both transparency of all terms of the Langevin displacement equation as well as a prescription for their determination. As an example, application of the methods developed, the real-time movement of an α-helix protein through a carbon nanotube is simulated.

In the present article, we show that the multilevel Monte Carlo method for elliptic stochastic partial differential equations can be interpreted as a sparse grid approximation. By using this interpretation, the method can straightforwardly be generalized to any given quadrature rule for high dimensional integrals like the quasi Monte Carlo method or the polynomial chaos approach. Besides the multilevel quadrature for approximating the solution's expectation, a simple and efficient modification of the approach is proposed to compute the stochastic solution's variance. Numerical results are provided to demonstrate and quantify the approach.

In two previous studies [J. Chem. Phys. 91, 1287 (1989); 95, 1234 (1991)] we had examined the dynamics of coupled, internal translational, and rotational motions in a rigid or pseudorigid N‐sphere macromolecular model using the rotational–translational Brownian dynamics algorithm of Dickinson et al. [J. Chem. Soc. Faraday Trans. 2 81, 591 (1985)]. In the present study, those works are generalized to include all possible internal flexible motions in an N‐sphere macromolecular model. In general, for the N‐sphere system there are 6(N‐1) degrees of configurational freedom, although not all modes may be active in any particular application. Using the language of small oscillation theory, the deviations in the generalized coordinates associated with the ‘‘joints’’ connecting the spheres to one another are described in terms of quadratic potentials. From these potentials, the components of the generalized forces (torques and forces) are obtained for subsequent use in the Brownian dynamics algorithm. The degree o...

In this article, a quality-control design framework that employs information for the supplier-buyer system is modeled. Significant operational savings may be obtained by using the integrated plans developed under this framework. This is especially true when the cost of a defective is high, and the variable sampling and rework costs are low. Analysis of the interaction of defective, rework, and variable sampling costs reveals that the savings are the result of a shift of control effort from the process-control to the lot-acceptance stage, which is the consequence of tradeoffs involving both stages. The managerial impact of adopting integrated plans is discussed.

In numerous physical processes involving the motion of micron and submicron sized particles near surfaces, such as the filtration of hydrosols and aerosols, the particle motion is the net result of the combined effects of fluid convection, external forces, particle inertia, Brownian particle motion, and particle-surface fluid dynamic interactions. The most general method of describing particle motion under the combined action of these effects is through the so-called Fokker-Planck equation. In the absence of particle-surface fluid dynamic interactions, the Fokker-Planck equation is well-known, and it has been applied in a general way to problems involving the adsorption or deposition of Brownian particles onto surfaces through a solution technique known as the Brownian dynamics simulation method. In this study, the Fokker-Planck equation for Brownian particle motion near surfaces is generalized to include particle-surface fluid dynamic interactions. The Fokker-Planck equation is shown to follow from the L...

Under sequential screening, a production lot is inspected item-by-item; the decision is made after inspecting each item whether to inspect another item or to reject the remainder of the lot; and thus uninspected items are never accepted. This screening process is a special case of the sequential sampling considered in Wortham and Wilson (1971). The process is formulated as an optimal stopping problem using a Bayesian approach. Based on an analysis of the structural properties of the optimal policy, a backward-recursive optimal algorithm, which is more efficient than the existing algorithm for optimal sequential sampling, is developed.