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Aptamers are structural single-stranded oligonucleotides generated in vitro to bind to a specific target molecule. Aptamers’ versatility can be enhanced with nucleic acid mimics (NAMs) during or after a selection process, also known as systematic evolution of ligands by exponential enrichment (SELEX). We address advantages and limitations of the technologies used to generate NAM aptamers, especially the applicability of existing engineered polymerases to replicate NAMs and methodologies to improve aptamers after SELEX. We also discuss the limitations of existing methods for sequencing NAM sequences and bioinformatic tools to predict NAM aptamer structures. As a conclusion, we suggest that NAM aptamers might successfully compete with molecular tools based on proteins such as antibodies for future application. Nucleic acid mimics (NAMs) add new conformational motifs and chemical groups that improve the binding affinity and stability of aptamers, boosting their applicability in vivo.De novo systematic evolution of ligands by exponential enrichment (SELEX) is limited by access to unnatural nucleotides and enzymes that can use unnatural nucleotides as substrates. Engineered polymerases can perform de novo selection of NAM aptamers, but the protocol still is complex and time consuming.The post-SELEX approach lacks the complexity of de novo SELEX because NAM aptamers are chemically synthetized. However, inserting unnatural nucleotides often disturbs aptamer binding interactions, and the effects of such modifications are difficult to establish.Computational tools to predict tertiary structure and docking elucidate aptamer–target interactions and allow tailored modifications that reduce the experimental time of the conventional trial-and-error approach.

The main focus of this paper is to develop the solutions for the higher order difference equations with factorials and discrete exponential functions. Using these concept, we get the unique solution for the trigonometric exponential function for the initial valued problem. These results are verified using the numerical calculations.

Purpose Exponential organizations (ExOs) are purpose-driven companies that leverage exponential technologies and exponential business practices to grow and scale rapidly, transform industries and create massive value and impact. In contrast, non-ExOs follow a linear approach to business and organizational strategy design and execution. This study aims to validate the hypothesis, based on financial metrics, that ExOs outperform their competitors and linear counterparts. Furthermore, it also brings a new understanding of the gap raised in the past eight years about how ExOs can achieve significantly better performance, measured with financial metrics. Design/methodology/approach For measuring how exponential an organization is, this study elaborated a completely new assessment tool called Exponential Quotient (ExQ). This study applied ExQ to the 100 largest US headquartered companies as ranked by Fortune magazine in 2014. Calculating the ExQ enabled this study to rank these Fortune 100 companies and identify the most and the least exponential firms. This study tracked these companies as to how they performed on different financial metrics over the eight years of 2014–2021 and analyzed the results. Findings Through the analysis, this study revealed that the top 10 ExOs have significantly outperformed their bottom 10 non-exponential peers, delivering 40x higher shareholder returns, 2.6x better revenue growth, 6.8x higher profitability and 11.7x better asset turnover. Furthermore, this study could identify commonalities and similarities between the two groups. This means that ExOs can thrive even in tough times and that accelerating technologies unlock abundance and allow every organization to become a disruptive innovator and stay ahead of the competition. These are novel results in the research focusing on the gap between exponential and traditional organizations. Research limitations/implications Using the ExQ diagnostics tool, every organization can see how flexible, scalable and agile they are, which is the starting point for an exponential transformation program. Although this approach has already found its way into practice and is applied globally by thousands of organizations (startups, scaleups and incumbents), so far, the academic establishment is in its nascent phase. With this research, the authors wanted to extend this field of science. On the other hand, because of its novelty, no appropriate previous studies existed to compare the results. Practical implications The possible implications showed that there is a plannable way for significantly increasing an organization’s ExQ and advance it from a linear toward an exponential organizational model. Originality/value The results validated the robustness of the ExO framework and philosophy and shed light on the importance of exponential transformation – a proven method to increase an organization’s ExQ. This framework is not a “how to be successful” guide. Instead, it uncovered some of the previously unknown and universal mechanisms of scalability – which, in turbulent times, make companies successful (based on financial metrics). To the best of the authors’ knowledge, this study was among the first kind of in-depth analyses to validate the whole ExO model.

First published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions.

We prove an inequality on decision trees on monotonic measures which generalizes the OSSS inequality on product spaces. As an application, we use this inequality to prove a number of new results on lattice spin models and their random-cluster representations. More precisely, we prove that For the Potts model on transitive graphs, correlations decay exponentially fast for β < β c . For the random-cluster model with cluster weight q ≥ 1 on transitive graphs, correlations decay exponentially fast in the subcritical regime and the cluster-density satisfies the mean-field lower bound in the supercritical regime. For the random-cluster models with cluster weight q ≥ 1 on planar quasi-transitive graphs 𝔾, p c ( 𝔾 ) p c ( 𝔾 * ) ( 1 - p c ( 𝔾 ) ) ( 1 - p c ( 𝔾 * ) ) = q As a special case, we obtain the value of the critical point for the square, triangular and hexagonal lattices. (This provides a short proof of a result of Beffara and the first author dating from 2012.) These results have many applications for the understanding of the subcritical (respectively disordered) phase of all these models. The techniques developed in this paper have potential to be extended to a wide class of models including the Ashkin-Teller model, continuum percolation models such as Voronoi percolation and Boolean percolation, super-level sets of massive Gaussian free field, and the random-cluster and Potts models with infinite range interactions.

With the spread of lubricating oils, the usage of viscosity becomes more and more significant in various industries. This essay is used to determine the relationship between viscosity and the change of concentration and temperature to avoid problems during production process. This research uses the high-degree function and exponential function to simulate the change trend of viscosity due to the two variables. Through research, the author discovered the exponential relationship between the temperature as well as concentration and viscosity of lubricating oils and other complex fluids. Based on the results of this research, the enterprise can also avoid excessive wear of the machine and high waste in the production process.

We establish a new decoupling inequality for curves in the spirit of earlier work of C. Demeter and the author which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in the work of Huxley. In particular, this leads to an improved bound |ζ(12+it)|≪t13/84+ε|\\zeta (\\frac {1}{2} + it)| \\ll t^{13/84 + \\varepsilon } for the zeta function on the critical line.

1. Dispersal is fundamental to ecological processes at all scales and levels of organization, but progress is limited by a lack of information about the general shape and form of plant dispersal kernels. We addressed this gap by synthesizing empirical data describing seed dispersal and fitting general dispersal kernels representing major plant types and dispersal modes. 2. A comprehensive literature search resulted in 107 papers describing 168 dispersal kernels for 144 vascular plant species. The data covered 63 families, all the continents except Antarctica, and the broad vegetation types of forest, grassland, shrubland and more open habitats (e.g. deserts). We classified kernels in terms of dispersal mode (ant, ballistic, rodent, vertebrates other than rodents, vehicle or wind), plant growth form (climber, graminoid, herb, shrub or tree), seed mass and plant height. 3. We fitted 11 widely used probability density functions to each of the 168 data sets to provide a statistical description of the dispersal kernel. The exponential power (ExP) and log-sech (LogS) functions performed best. Other 2-parameter functions varied in performance. For example, the log-normal and Weibull performed poorly, while the 2Dt and power law performed moderately well. Of the single-parameter functions, the Gaussian performed very poorly, while the exponential performed better. No function was among the best-fitting for all data sets. 4. For 10 plant growth form/dispersal mode combinations for which we had >3 data sets, we fitted ExP and LogS functions across multiple data sets to provide generalized dispersal kernels. We also fitted these functions to subdivisions of these growth form/dispersal mode combinations in terms of seed mass (for animal-dispersed seeds) or plant height (wind-dispersed) classes. These functions provided generally good fits to the grouped data sets, despite variation in empirical methods, local conditions, vegetation type and the exact dispersal process. 5. Synthesis. We synthesize the rich empirical information on seed dispersal distances to provide standardized dispersal kernels for 168 case studies and generalized kernels for plant growth form/dispersal mode combinations. Potential uses include the following: (i) choosing appropriate dispersal functions in mathematical models; (ii) selecting informative dispersal kernels for one's empirical study system; and (iii) using representative dispersal kernels in cross-taxon comparative studies.