A Simple Statistical Mechanical Model for Pressure Induced Ionization

An extremely simple univariate statistical model called ‘IndOzy’ was developed to predict El Niño‐Southern Oscillation (ENSO) events. The model uses five delayed‐time inputs of the Niño 3.4 sea surface temperature anomaly (SSTA) index to predict up to 12 months in advance. The prediction skill of the model was assessed using both short‐ and long‐term indices and compared with other operational dynamical and statistical models. Using ENSO‐CLIPER(climatology and persistence) as benchmark, only a few statistical models including IndOzy are considered skillful for short‐range prediction. All models, however, do not differ significantly from the benchmark model at seasonal Lead‐3–6. None of the models show any skill, even against a no‐skill random forecast, for seasonal Lead‐7. When using the Niño 3.4 SSTA index from 1856 to 2005, the ultra simple IndOzy shows a useful prediction up to 4 months lead, and is slightly less skillful than the best dynamical model LDEO5. That such a simple model such as IndOzy, which can be run in a few seconds on a standard office computer, can perform comparably with respect to the far more complicated models raises some philosophical questions about modelling extremely complicated systems such as ENSO. It seems evident that much of the complexity of many models does little to improve the accuracy of prediction. If larger and more complex models do not perform significantly better than an almost trivially simple model, then perhaps future models that use even larger data sets, and much greater computer power may not lead to significant improvements in both dynamical and statistical models. Investigating why simple models perform so well may help to point the way to improved models. For example, analysing dynamical models by successively stripping away their complexity can focus in on the most important parameters for a good prediction. Copyright © 2007 Royal Meteorological Society

Local signals in the energy landscape of collapsed helical proteins

The behavior of the inter-ionic potential of condensed liquid cesium in a wide temperature range

Historically, the development of equations of state for fluids has almost invariably followed the lead of the van der Waals (vdW) equation which includes an attraction term and a repulsion term. In this paper, using a simple statistical mechanics model, we introduce a parameter σ as both the power and a coefficient of the packing fraction y which locates at the numerator of the vdW attraction term. Then nine equations of state are constructed to solve the critical conditions and the main thermodynamic properties of pure substances at liquid-vapor equilibrium. As a result, the correct critical compressibility factors of Nitrogen, Argon, Carbon dioxide, Ethene, Methane, Oxygen, Propene, Water and Hydrogen, are obtained with an optimal choice of parameter σ. Good predictions of these equations to the liquid-vapor equilibrium properties below critical temperature are reported and compared with experimental data.

Following a review of the problem of stilbene isomerism an account is given of recent picosecond tinescale experiments on this system.Transient absorption methods are used to expose vibrational relaxation details for molecules in solution and streak camera measurements of fluorescence decay are presented to demonstrate the irreversibility of the Si (trans) decay.A simple statistical mechanical model is presented to describe the effect of viscosity on the twisting dynamics of trans-stilbene.A summary of recent experiments involving stilbene in the gas phase is presented.The isolated molecules twist very rapidly (15 ps at 265 nm excitation) and display characteristics typical of systems with a potential barrier.Finally the solution and gas phase processes are contrasted. INTRODUCTORY REVIEWIt is well known that substituted ethylenes can undergo cis-trans isomerism following optical excitation.A large literature already exists on this topic and the particular case of stilbenes (1,2-diphenylethylenes) was recently reviewed by Saltiel and coworkers (1).Phenyl substituted ethylenes received considerable attention from photochenists because their optical spectra are in the near ultraviolet, readily accessible to traditional light sources.The groundwork for understanding the photoisomerisn process in solutions was laid on the basis of conventional (pre-laser) experiments (1,2) but the intrinsic molecular steps involved are now known from vapor phase studies to be subnanosecond (3,4).The basic model for the isomerism is that a twisted, less conjugated form of tilbene is formed following optical excitation (5) .This twisted form may then undergo relaxation processes that result in both cis and trans structures (6).The solvent slows down the isomerization and at sufficiently low temperature or high viscosity the rate is found to be even slower than the natural radiative processes (7).The fluorescent properties of the system therefore can be used to monitor the isonerization.Saltiel and coworkers (8,9) have shown that the principal ultraviolet photochemistry of stilbeme arises from the singlet excited surface.The triplet state can be involved when sensitizers are present (9,10), and the ground state pathway requires moderately high temperatures (1,2).There is also evidence that isomerization is not the exclusive photoprocess since small yields of rearranged species have been reported (11).

In a simple nonequilibrium statistical mechanics model (two coupled nonlinear stochastic reaction-diffusion equations), self-sustained oscillations appear as a symmetry-breaking effect for the associated probability density. Correlation and response functions are approximately calculated above and below the transition point. Renormalization-group theory yields the leading-order scaling of order parameter, relaxation time, correction to the collective frequency, and correlation length.

Several key problems previously analyzed by simulated annealing are well described by a simple two-state statistical mechanical model, equivalent to the one-dimensional Ising model, in conjunction with an Arrhenius type rate equation. With this model we develop an analytic solution for the optimal cooling strategy which computationally is much faster than the previously developed adaptive algorithm. In the long time limit the analytic solution reduces to the one cooling schedule which is sure to reach the ground state. Our model predictions are in good agreement with earlier numerical simulation results for optimal cooling schedules as well as for stationary and dynamic properties of system energy, heat capacity, and relaxation time.

Understanding the mechanism of protein secondary structure formation is an essential part of the protein-folding puzzle. Here, we describe a simple statistical mechanical model for the formation of a beta-hairpin, the minimal structural element of the antiparallel beta-pleated sheet. The model accurately describes the thermodynamic and kinetic behavior of a 16-residue, beta-hairpin-forming peptide, successfully explaining its two-state behavior and apparent negative activation energy for folding. The model classifies structures according to their backbone conformation, defined by 15 pairs of dihedral angles, and is further simplified by considering only the 120 structures with contiguous stretches of native pairs of backbone dihedral angles. This single sequence approximation is tested by comparison with a more complete model that includes the 2(15) possible conformations and 15 x 2(15) possible kinetic transitions. Finally, we use the model to predict the equilibrium unfolding curves and kinetics for several variants of the beta-hairpin peptide.

Over 80% of the vast reserves of Alberta's oil sands can be produced only by using in situ recovery methods. Among them, which is likely the most efficient and important, is the Steam-Assisted Gravity Drainage (SAGD) process. Numerical simulation allows for a practical way of predicting reservoir performance using the SAGD process during the whole field development cycle. However, in the earlier stages of development studies, when it is necessary to undertake preliminary engineering design, estimate reserves, evaluate the project against other SAGD prospects, as well as consider the uncertainty of some reservoir parameters, it may not be feasible to do a detailed simulation study due to the long computational time involved in a SAGD process simulation. Under these circumstances, a method for predicting reservoir performance using a simple statistical model that can approximate the reservoir simulator over a given range of some important input parameters is a good approach to provide the means of comparison and preliminary predictions without resorting to numerical simulation. The purpose of this work is to use 'experimental design' techniques to develop a response surface that can predict SAGD performance without the expense of doing simulation. A preliminary screening study was done in order to select the most influential variables on SAGD performance. The variables used for that purpose include reservoir rock/fluid properties, such as reservoir thickness, porosity, vertical permeability, horizontal-vertical permeability ratio, methane content, rock thermal conductivity, initial oil saturation and bitumen viscosity, along with SAGD design and operating variables, including spacing between injector/producer, operating pressure, preheating period, maximum steam injection rate and SAGD well pattern spacing. In a second stage, the influential variables were used to create a statistically significant correlation by using the experimental design method and response surface techniques. This simple model allows the prediction of the SAGD performance in terms of maximum net present value (NPV) over 15 years of project life, for a given range of the most influential parameters. Introduction Numerical simulation of complex systems such as SAGD processes require long computational times due to the compositional nature and transient temperature behaviour of the models used in the solution. Longer simulation times lead to either a delay in the decision-making process or to biased forecasts and sub-optimal decisions, since unpractical times would be required to span all possible scenarios in which a SAGD process can be developed. This is particularly important at the earliest field development stages when the high uncertainty of some reservoir and operational parameters is a significant constraint. Transference of uncertainty from the reservoir and operational parameters to the forecast variables during a SAGD process using numerical simulation is almost an impossible and very expensive task. To overcome this situation, engineers need simple models to predict SAGD performance. As an alternative, this work proposes a "Response Surface Correlation" generated by experimental design techniques and response surface methodology. Such a correlation will substitute the reservoir simulator in a given operating domain in order to account for all necessary cases needed to quantify and transfer the reservoir uncertainty to a SAGD performance variable.

Machine learning (ML) often provides applicable high-performance models to facilitate decision-makers in various fields. However, this high performance is achieved at the expense of the interpretability of these models, which has been criticized by practitioners and has become a significant hindrance in their application. Therefore, in highly sensitive decisions, black boxes of ML models are not recommended. We proposed a novel methodology that uses complex supervised ML models and transforms them into simple, interpretable, transparent statistical models. This methodology is like stacking ensemble ML in which the best ML models are used as a base learner to compute relative feature weights. The index of these weights is further used as a single covariate in the simple logistic regression model to estimate the likelihood of an event. We tested this methodology on the primary dataset related to cardiovascular diseases (CVDs), the leading cause of mortalities in recent times. Therefore, early risk assessment is an important dimension that can potentially reduce the burden of CVDs and their related mortality through accurate but interpretable risk prediction models. We developed an artificial neural network and support vector machines based on ML models and transformed them into a simple statistical model and heart risk scores. These simplified models were found transparent, reliable, valid, interpretable, and approximate in predictions. The findings of this study suggest that complex supervised ML models can be efficiently transformed into simple statistical models that can also be validated.

Protein chains coil into alpha-helices and beta-sheet structures. Knowing the timescales and mechanism of formation of these basic structural elements is essential for understanding how proteins fold. For the past 40 years, alpha-helix formation has been extensively investigated in synthetic and natural peptides, including by nanosecond kinetic studies. In contrast, the mechanism of formation of beta structures has not been studied experimentally. The minimal beta-structure element is the beta-hairpin, which is also the basic component of antiparallel beta-sheets. Here we use a nanosecond laser temperature-jump apparatus to study the kinetics of folding a beta-hairpin consisting of 16 amino-acid residues. Folding of the hairpin occurs in 6 micros at room temperature, which is about 30 times slower than the rate of alpha-helix formation. We have developed a simple statistical mechanical model that provides a structural explanation for this result. Our analysis also shows that folding of a beta-hairpin captures much of the basic physics of protein folding, including stabilization by hydrogen bonding and hydrophobic interactions, two-state behaviour, and a funnel-like, partially rugged energy landscape.

In many cases, transcriptional regulation involves the binding of transcription factors at sites on the DNA that are not immediately adjacent to the promoter of interest. This action at a distance is often mediated by the formation of DNA loops: Binding at two or more sites on the DNA results in the formation of a loop, which can bring the transcription factor into the immediate neighborhood of the relevant promoter. These processes are important in settings ranging from the historic bacterial examples (bacterial metabolism and the lytic-lysogeny decision in bacteriophage), to the modern concept of gene regulation to regulatory processes central to pattern formation during development of multicellular organisms. Though there have been a variety of insights into the combinatorial aspects of transcriptional control, the mechanism of DNA looping as an agent of combinatorial control in both prokaryotes and eukaryotes remains unclear. We use single-molecule techniques to dissect DNA looping in the lac operon. In particular, we measure the propensity for DNA looping by the Lac repressor as a function of the concentration of repressor protein and as a function of the distance between repressor binding sites. As with earlier single-molecule studies, we find (at least) two distinct looped states and demonstrate that the presence of these two states depends both upon the concentration of repressor protein and the distance between the two repressor binding sites. We find that loops form even at interoperator spacings considerably shorter than the DNA persistence length, without the intervention of any other proteins to prebend the DNA. The concentration measurements also permit us to use a simple statistical mechanical model of DNA loop formation to determine the free energy of DNA looping, or equivalently, the for looping.

The lateral motion of ground vehicles is characterized by the rolling contact between wheels and guideway. Railway vehicles feature passive lateral guidance by wheelsets while road vehicles handling is operated by steering devices. Lateral dynamics is an extremely complex problem but the fundamental behavior can already understood by simplified mechanical models. In this paper the historical development of modeling approaches for lateral vehicle dynamics is reviewed and presented by multibody dynamics techniques. It is shown that simplified models are very useful as benchmarks for checking more complex systems. Applying the same assumptions for modeling and simulation, the fundamental results have to tally with each other.

Abstract. Much has been written about the so-called hiatus or pause in global warming, also known as the stasis period, the start of which is typically dated to 1998. HadCRUT4 global mean temperatures slightly decreased over the 1998–2013 period, although a simple statistical model predicts that they should have grown by 0.016 ∘C/yr, in proportion to the increases in the concentrations of well-mixed greenhouse gases (WMGHGs) and ozone. We employ a statistical approach to assess the contributions of model forcings and natural variability to the hiatus. Our point estimates suggest that none of the model forcings explain more than one-third of the missing heat, accounting for the upper bound of the confidence interval on the effect of tropospheric aerosols, which is the most prominent yet most uncertainly measured of the model forcings that could explain the missing heat. The El Niño–Southern Oscillation (ENSO) explains up to about one-third of the missing heat, and two-thirds and possibly up to 81 % is explained by the unusually high temperature of 1998. Looking forward, the simple model also fails to explain the large increases since then (0.087 ∘C/yr from 2013 to 2016). This period coincides with another El Niño, but the ENSO fails to satisfactorily account for the increase. Instead, we propose a semiparametric cointegrating statistical model that augments an energy balance model with a novel multi-basin measure of the oceans' multidecadal temperature cycles. The model partially explains the recent slowdown and explains all of the subsequent warming. The natural cycle suggests the possibility – depending in part on the rate of increase of WMGHG concentrations – of a much longer hiatus over the period from roughly 2023 to 2061, with potentially important implications for policy evaluation.

PM10 is one of the aerosol particles that can endanger human health. This research conducted by forcasteing for PM10 concentration. Forecasting is an activity of estimating or predicting events in the future, therefore it is necessary to do analysis simple statistical model to know goog results. In this case, several forecasting models are used for the daily PM10 concentration in Kototabang, that is Liniear, Quadratic, and Exponential Trend Model. As the results of this research, monthly forecasting using Linear Trend Model has the highest correlation value in October (-60) with MAD value 0.254, MSE 0.0651, RMSE 0.255, and MAPE 1848.8. Monthly forecasting using the Quadratic Trend Model has the highest correlation value in February (+0.52) with MAD value 0.013, MSE 0.0002, RMSE 0.015, and MAPE 103.934. then, for monthly forecasting using the Exponential Trend Model has the highest value in October (+0.61) with MAD value 0.124, MSE 0.0154, RMSE 0.124, and MAPE 893.484. the output of the forecasting model obtained the best model for forecasting the daily PM10 concentration in Kototabang i.e by using a simple statistical model, linear trend model.