Large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes

In this paper we prove exact forms of large deviations for local times and intersection local times of fractional Brownian motions and Riemann-Liouville processes. We also show that a fractional Brownian motion and the related Riemann-Liouville process behave like constant multiples of each other with regard to large deviations for their local and intersection local times. As a consequence of our large deviation estimates, we derive laws of iterated logarithm for the corresponding local times. The key points of our methods: (1) logarithmic superadditivity of a normalized sequence of moments of exponentially randomized local time of a fractional Brownian motion; (2) logarithmic subadditivity of a normalized sequence of moments of exponentially randomized intersection local time of Riemann-Liouville processes; (3) comparison of local and intersection local times based on embedding of a part of a fractional Brownian motion into the reproducing kernel Hilbert space of the Riemann-Liouville process.Comment: To appear in the Annals of Probabilit

Oxidized Forms of Antiaromatic Oligomers of Biphenylene

Rsumen de la comunicaciónThe importance of antiaromatic molecules in Chemistry and more recently in material science is rising. In the particular case of applications in electronics, the antiaromatic skeleton offers the favorable situation of high energy (i.e., destabilized) occupied molecular orbitals allowing to ease oxidation, doping or electron transfer to form conductive and photo-active substrates.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Some Results on Critical (P5,HP_5,H)-free Graphs

Given two graphs $H_1$ and $H_2$, a graph is $(H_1,H_2)$-free if it contains no induced subgraph isomorphic to $H_1$ nor $H_2$. A graph $G$ is $k$-vertex-critical if every proper induced subgraph of $G$ has chromatic number less than $k$, but $G$ has chromatic number $k$. The study of $k$-vertex-critical graphs for specific graph classes is an important topic in algorithmic graph theory because if the number of such graphs that are in a given hereditary graph class is finite, then there exists a polynomial-time certifying algorithm to decide the $k$-colorability of a graph in the class. In this paper, we show that: (1) for $k \ge 1$, there are finitely many $k$-vertex-critical $(P_5,K_{1,4}+P_1)$-free graphs; (2) for $s \ge 1$, there are finitely many 5-vertex-critical $(P_5,K_{1,s}+P_1)$-free graphs; (3) for $k \ge 1$, there are finitely many $k$-vertex-critical $(P_5,\overline{K_3+2P_1})$-free graphs. Moreover, we characterize all $5$-vertex-critical $(P_5,H)$-free graphs where $H \in \{K_{1,3}+P_1,K_{1,4}+P_1,\overline{K_3+2P_1}\}$ using an exhaustive graph generation algorithm.Comment: arXiv admin note: substantial text overlap with arXiv:2308.03414; text overlap with arXiv:2211.0417

Critical (P5,dart)(P_5,dart)-Free Graphs

Given two graphs $H_1$ and $H_2$, a graph is $(H_1,H_2)$-free if it contains no induced subgraph isomorphic to $H_1$ nor $H_2$. Let $P_t$ be the path on $t$ vertices. A dart is the graph obtained from a diamond by adding a new vertex and making it adjacent to exactly one vertex with degree 3 in the diamond. In this paper, we show that there are finitely many $k$-vertex-critical $(P_5,dart)$-free graphs for $k \ge 1$ To prove these results, we use induction on $k$ and perform a careful structural analysis via Strong Perfect Graph Theorem combined with the pigeonhole principle based on the properties of vertex-critical graphs. Moreover, for $k \in \{5, 6, 7\}$ we characterize all $k$-vertex-critical $(P_5,dart)$-free graphs using a computer generation algorithm. Our results imply the existence of a polynomial-time certifying algorithm to decide the $k$-colorability of $(P_5,dart)$-free graphs for $k \ge 1$ where the certificate is either a $k$-coloring or a $(k+1)$-vertex-critical induced subgraph.Comment: arXiv admin note: text overlap with arXiv:2211.0417

A GPU-accelerated package for simulation of flow in nanoporous source rocks with many-body dissipative particle dynamics

Mesoscopic simulations of hydrocarbon flow in source shales are challenging, in part due to the heterogeneous shale pores with sizes ranging from a few nanometers to a few micrometers. Additionally, the sub-continuum fluid-fluid and fluid-solid interactions in nano- to micro-scale shale pores, which are physically and chemically sophisticated, must be captured. To address those challenges, we present a GPU-accelerated package for simulation of flow in nano- to micro-pore networks with a many-body dissipative particle dynamics (mDPD) mesoscale model. Based on a fully distributed parallel paradigm, the code offloads all intensive workloads on GPUs. Other advancements, such as smart particle packing and no-slip boundary condition in complex pore geometries, are also implemented for the construction and the simulation of the realistic shale pores from 3D nanometer-resolution stack images. Our code is validated for accuracy and compared against the CPU counterpart for speedup. In our benchmark tests, the code delivers nearly perfect strong scaling and weak scaling (with up to 512 million particles) on up to 512 K20X GPUs on Oak Ridge National Laboratory's (ORNL) Titan supercomputer. Moreover, a single-GPU benchmark on ORNL's SummitDev and IBM's AC922 suggests that the host-to-device NVLink can boost performance over PCIe by a remarkable 40\%. Lastly, we demonstrate, through a flow simulation in realistic shale pores, that the CPU counterpart requires 840 Power9 cores to rival the performance delivered by our package with four V100 GPUs on ORNL's Summit architecture. This simulation package enables quick-turnaround and high-throughput mesoscopic numerical simulations for investigating complex flow phenomena in nano- to micro-porous rocks with realistic pore geometries

Dilepton Yield in Heavy-Ion Collisions with Bose Enhancement of Decay Width

The excess of low invariant mass dilepton yield in heavy ion collisions arising from reduction in the rho meson mass at finite temperatures is partially suppressed because of the effect on the width of the rho meson induced by Bose enhancement, essentially due to emission of pions in a medium of the pion gas in the central rapidity region. The sensitivity of the effect on the initial temperature of the hadronic phase is also examined.Comment: Plain latex fil

A unified generation-registration framework for improved MR-based CT synthesis in proton therapy.

BACKGROUND The use of magnetic resonance (MR) imaging for proton therapy treatment planning is gaining attention as a highly effective method for guidance. At the core of this approach is the generation of computed tomography (CT) images from MR scans. However, the critical issue in this process is accurately aligning the MR and CT images, a task that becomes particularly challenging in frequently moving body areas, such as the head-and-neck. Misalignments in these images can result in blurred synthetic CT (sCT) images, adversely affecting the precision and effectiveness of the treatment planning. PURPOSE This study introduces a novel network that cohesively unifies image generation and registration processes to enhance the quality and anatomical fidelity of sCTs derived from better-aligned MR images. METHODS The approach synergizes a generation network (G) with a deformable registration network (R), optimizing them jointly in MR-to-CT synthesis. This goal is achieved by alternately minimizing the discrepancies between the generated/registered CT images and their corresponding reference CT counterparts. The generation network employs a UNet architecture, while the registration network leverages an implicit neural representation (INR) of the displacement vector fields (DVFs). We validated this method on a dataset comprising 60 head-and-neck patients, reserving 12 cases for holdout testing. RESULTS Compared to the baseline Pix2Pix method with MAE 124.95 30.74 HU, the proposed technique demonstrated 80.98 7.55 HU. The unified translation-registration network produced sharper and more anatomically congruent outputs, showing superior efficacy in converting MR images to sCTs. Additionally, from a dosimetric perspective, the plan recalculated on the resulting sCTs resulted in a remarkably reduced discrepancy to the reference proton plans. CONCLUSIONS This study conclusively demonstrates that a holistic MR-based CT synthesis approach, integrating both image-to-image translation and deformable registration, significantly improves the precision and quality of sCT generation, particularly for the challenging body area with varied anatomic changes between corresponding MR and CT