In the present paper, we study the asymptotic properties of the semi-exponential operator connected with p( x) =x^3 . The main result is a pointwise complete asymptotic expansion valid for locally smooth functions of exponential growth. All coefficients are derived and explicitly given. Furthermore, we characterize classes of functions f for which the semi-exponential operator connected with p( x) =x^3 provides asymptotically a better approximation than the corresponding operator of exponential type. Finally, we present numerical examples which illustrate the better rate of convergence.
We present a novel space-efficient graph coarsening technique for $n$-vertex planar graphs $G$, called \textit{cloud partition}, which partitions the vertices $V(G)$ into disjoint sets $C$ of size $O(\log n)$ such that each $C$ induces a connected subgraph of $G$. Using this partition $\mathcal{P}$ we construct a so-called \textit{structure-maintaining minor} $F$ of $G$ via specific contractions within the disjoint sets such that $F$ has $O(n/\log n)$ vertices. The combination of $(F, \mathcal{P})$ is referred to as a \textit{cloud decomposition}. For planar graphs we show that a cloud decomposition can be constructed in $O(n)$ time and using $O(n)$ bits. Given a cloud decomposition $(F, \mathcal{P})$ constructed for a planar graph $G$ we are able to find a balanced separator of $G$ in $O(n/\log n)$ time. Contrary to related publications, we do not make use of an embedding of the planar input graph. We generalize our cloud decomposition from planar graphs to $H$-minor-free graphs for any fixed graph $H$. This allows us to construct the succinct encoding scheme for $H$-minor-free graphs due to Blelloch and Farzan (CPM 2010) in $O(n)$ time and $O(n)$ bits improving both runtime and space by a factor of $\Theta(\log n)$. As an additional application of our cloud decomposition we show that, for $H$-minor-free graphs, a tree decomposition of width $O(n^{1/2 + \epsilon})$ for any $\epsilon > 0$ can be constructed in $O(n)$ bits and a time linear in the size of the tree decomposition. A similar result by Izumi and Otachi (ICALP 2020) constructs a tree decomposition of width $O(k \sqrt{n} \log n)$ for graphs of treewidth $k \leq \sqrt{n}$ in sublinear space and polynomial time.
BACKGROUND:Advanced external photon beam radiotherapy requires dosimetry detectors with high spatial resolution and minimal perturbation effects. Silicon diode detectors are widely used due to their high sensitivity and small sensitive volumes, but fluence perturbation effects and energy dependence can affect performance and depend on detector construction. Shielded and unshielded configurations are used to address these challenges, but their clinical performance and limitations require systematic evaluation. PURPOSE:This study aims to evaluate the clinical performance of two newly developed silicon diode detectors-SunSILICON (unshielded) and SunSILICON P (shielded)-for relative dosimetry in external photon beam radiotherapy. The detectors' response behaviors are compared to established detectors across the full clinical range of field sizes and beam energies, focusing on percentage depth dose (PDD) and lateral beam profile measurements. METHODS:PDD and lateral beam profile measurements across the full range of clinical field sizes were performed on Varian TrueBeam and Elekta Versa HD clinical linear accelerators with photon energies ranging from 4 to 25 MV, as well as a Nordion Eldorado 6 60Co unit, using various types of motorized water phantoms. Comparative measurements were performed with ionization chambers, as well as other silicon and diamond detectors. Over 600 scans were analyzed, and gamma analysis was applied to assess agreement using 0.5%/0.5 mm for PDDs and 1%/1 mm for lateral beam profiles. Angular dependence, detector sensitivity and the effective point of measurement (EPOM) were determined in solid phantoms. RESULTS:SunSILICON and SunSILICON P demonstrated excellent agreement with established detectors within their specified field size ranges. Gamma passing rates exceeded 99% for most comparisons, with minor deviations in large fields or at field size limits. The shielded SunSILICON P showed reduced energy dependence in large fields compared to the unshielded version, while SunSILICON showed superior performance in small fields. Both detectors exhibited minimal angular dependence (<1% for clinically relevant angles) and negligible intra-type variation. The measured EPOMs matched calculated values within uncertainty. The combination of both detectors enables comprehensive coverage of clinical dosimetry needs. CONCLUSIONS:SunSILICON and SunSILICON P provide reliable, high-resolution dosimetry for external photon beam radiotherapy across a broad range of clinical scenarios. Their performance is comparable to or exceeds that of established silicon and diamond detectors, with the shielded version particularly suited for larger fields due to its reduced energy dependence. Together, these detectors offer a robust solution for clinical relative dosimetry.
Farming has evolved from the basic irrigation techniques used in ancient river valley civilizations to the sophisticated Precision Agriculture of today, playing an important role in the advancement of human society. This paper explores the use of Machine Learning and Deep Learning algorithms in Precision Agriculture, an essential task in agriculture that helps ensure a stable food supply and improves the efficiency of food production. Despite advances in Precision Agriculture and the widespread adoption of Machine Learning and Deep Learning algorithms, a comprehensive review that systematically addresses the challenges of data quality, model interoperability, and multisource data integration in Precision Agriculture is still lacking. To bridge this gap, we conducted a systematic review of more than 100 studies published between 2021 and 2024. Our analysis focuses on the application of several Machine Learning and Deep Learning algorithms, such as Artificial Neural Networks, Support Vector Machines, Convolutional Neural Networks, and Random Forests. Using a comparative analysis methodology, we identify key features influencing Precision Agriculture, such as temperature, rainfall, remote sensing data, and soil types. Our findings highlight ongoing challenges in standardizing data protocols and developing Explainable AI models that can be generalized across diverse agricultural conditions. The key takeaway is that integrating IoT with real-time data processing can significantly improve agricultural resilience and efficiency. Future research should focus on refining robust models and expanding multisource data integration to effectively address these challenges.
BACKGROUND:Field output factor measurements of clinical linear accelerators require detector-specific corrections, due to the introduction of fluence perturbation effects by non-water-equivalent components of applied detectors. PURPOSE:This study aims to determine field output correction factors for novel shielded and unshielded silicon diode detectors in high energy photon fields. Special emphasis is placed on understanding the influence of perturbation factors and evaluating the suitability of these detectors across a wide range of field sizes. METHODS:Field output correction factors for the silicon diodes SunSILICON and SunSILICON P were determined through experimental measurements conducted at four distinct sites. Monte Carlo-based models of the diode detectors were developed to calculate field output correction factors using the EGSnrc code system. In addition, these silicon diode models enabled a detailed analysis of perturbation factors for field sizes from 0.6 cm up to 40 cm. RESULTS:Experimentally determined and Monte Carlo calculated field output correction factors are in good agreement for the detectors investigated. The perturbation factor analysis demonstrated a strong field size dependence of the fluence perturbation factor for silicon. CONCLUSION:This is the first study to systematically characterize the SunSILICON diode detector family using both simulation and measurement. The findings confirm that both shielded and unshielded designs are suitable for clinical dosimetry in photon beams, requiring only minor corrections. The shielding of the SunSILICON P diode enables accurate field output factor measurements across a broad range of field sizes, establishing its utility in modern radiotherapy applications.
