Trajectory planning optimization for real-time 6DOF robotic patient motion compensation

We present for the first time a general 6DoF trajectory planning method that can be used in real-time image guided radiation therapy procedures for robotic stabilization of dynamically moving tumor targets. As the radiation beam is always on during the motion compensation process, it is mandatory that the 6D correction trajectory is optimal both spatially and temporally in order to maximize radiation to the tumor and minimize unintentional irradiation of healthy tissues. Unlike prior works, which relied on motion control approaches as PID or other controllers, this work presents the concept of motion planning, where all potential 6D trajectories are searched using ultrafast optimization methods and the best trajectory is chosen. As the method formulates the problem as an objective function to be solved, it allows high flexibility in that users can optimize various performance requirements such as mechanical robot limits, patient velocities, or other aspects that must operate within certain limits in order to ensure a safe medical process

A conceptual study on real-time adaptive radiation therapy optimization through ultra-fast beamlet control

A central problem in the field of radiation therapy (RT) is how to optimally deliver dose to a patient in a way that fully accounts for anatomical position changes over time. As current RT is a static process, where beam intensities are calculated before the start of treatment, anatomical deviations can result in poor dose conformity. To overcome these limitations, we present a simulation study on a fully dynamic real-time adaptive radiation therapy (RT-ART) optimization approach that uses ultra-fast beamlet control to dynamically adapt to patient motion in real-time. A virtual RT-ART machine was simulated with a rapidly rotating linear accelerator (LINAC) source (60 RPM) and a binary 1D multi-leaf collimator (MLC) operating at 100 Hz. If the real-time tracked target motion exceeded a predefined threshold, a time dependent objective function was solved using fast optimization methods to calculate new beamlet intensities that were then delivered to the patient. To evaluate the approach, system response was analyzed for patient derived continuous drift, step-like, and periodic intra-fractional motion. For each motion type investigated, the RT-ART method was compared against the ideal case with no patient motion (static case) as well as to the case without the use RT-ART. In all cases, isodose lines and dose-volume-histograms (DVH) showed that RT-ART plan quality was approximately the same as the static case, and considerably better than the no RT-ART case. The RT-ART optimization framework has the potential to optimally deliver dose to a patient in a way that fully accounts for anatomical changes due to motion. With continued advances in real-time patient motion tracking and fast computational processes, there is significant potential for the RT-ART optimization process to be realized on next generation RT machines

HH-Decomposition of rr-graphs when HH is an rr-graph with exactly kk independent edges

Let $\phi_H^r(n)$ be the smallest integer such that, for all $r$-graphs $G$ on $n$ vertices, the edge set $E(G)$ can be partitioned into at most $\phi_H^r(n)$ parts, of which every part either is a single edge or forms an $r$-graph isomorphic to $H$. The function $\phi^2_H(n)$ has been well studied in literature, but for the case $r\ge 3$, the problem that determining the value of $\phi_H^r(n)$ is widely open. Sousa (2010) gave an asymptotic value of $\phi_H^r(n)$ when $H$ is an $r$-graph with exactly 2 edges, and determined the exact value of $\phi_H^r(n)$ in some special cases. In this paper, we first give the exact value of $\phi_H^r(n)$ when $H$ is an $r$-graph with exactly 2 edges, which improves Sousa's result. Second we determine the exact value of $\phi_H^r(n)$ when $H$ is an $r$-graph consisting of exactly $k$ independent edges

Decomposition of Graphs into (k,r)(k,r)-Fans and Single Edges

Let $\phi(n,H)$ be the largest integer such that, for all graphs $G$ on $n$ vertices, the edge set $E(G)$ can be partitioned into at most $\phi(n, H)$ parts, of which every part either is a single edge or forms a graph isomorphic to $H$. Pikhurko and Sousa conjectured that \phi(n,H)=\ex(n,H) for \chi(H)\geqs3 and all sufficiently large $n$, where \ex(n,H) denotes the maximum number of edges of graphs on $n$ vertices that does not contain $H$ as a subgraph. A $(k,r)$-fan is a graph on $(r-1)k+1$ vertices consisting of $k$ cliques of order $r$ which intersect in exactly one common vertex. In this paper, we verify Pikhurko and Sousa's conjecture for $(k,r)$-fans. The result also generalizes a result of Liu and Sousa.Comment: 18 page

Extremal graph for intersecting odd cycles

An extremal graph for a graph $H$ on $n$ vertices is a graph on $n$ vertices with maximum number of edges that does not contain $H$ as a subgraph. Let $T_{n,r}$ be the Tur\'{a}n graph, which is the complete $r$-partite graph on $n$ vertices with part sizes that differ by at most one. The well-known Tur\'{a}n Theorem states that $T_{n,r}$ is the only extremal graph for complete graph $K_{r+1}$. Erd\"{o}s et al. (1995) determined the extremal graphs for intersecting triangles and Chen et al. (2003) determined the maximum number of edges of the extremal graphs for intersecting cliques. In this paper, we determine the extremal graphs for intersecting odd cycles

On Dark Energy Isocurvature Perturbation

Determining the equation of state of dark energy with astronomical observations is crucially important to understand the nature of dark energy. In performing a likelihood analysis of the data, especially of the cosmic microwave background and large scale structure data the dark energy perturbations have to be taken into account both for theoretical consistency and for numerical accuracy. Usually, one assumes in the global fitting analysis that the dark energy perturbations are adiabatic. In this paper, we study the dark energy isocurvature perturbation analytically and discuss its implications for the cosmic microwave background radiation and large scale structure. Furthermore, with the current astronomical observational data and by employing Markov Chain Monte Carlo method, we perform a global analysis of cosmological parameters assuming general initial conditions for the dark energy perturbations. The results show that the dark energy isocurvature perturbations are very weakly constrained and that purely adiabatic initial conditions are consistent with the data.Comment: Published in JCAP 201

Odd induced subgraphs in graphs with treewidth at most two

A long-standing conjecture asserts that there exists a constant $c>0$ such that every graph of order $n$ without isolated vertices contains an induced subgraph of order at least $cn$ with all degrees odd. Scott (1992) proved that every graph $G$ has an induced subgraph of order at least $|V(G)|/(2\chi(G))$ with all degrees odd, where $\chi(G)$ is the chromatic number of $G$, this implies the conjecture for graphs with { bounded} chromatic number. But the factor $1/(2\chi(G))$ seems to be not best possible, for example, Radcliffe and Scott (1995) proved $c=\frac 23$ for trees, Berman, Wang and Wargo (1997) showed that $c=\frac 25$ for graphs with maximum degree $3$, so it is interesting to determine the exact value of $c$ for special family of graphs. In this paper, we further confirm the conjecture for graphs with treewidth at most 2 with $c=\frac{2}{5}$, and the bound is best possible.Comment: 13 page

Prime ideals in decomposable lattices

A distributive lattice $L$ with minimum element $0$ is called decomposable lattice if $a$ and $b$ are not comparable elements in $L$ there exist $\overline{a},\overline{b}\in L$ such that $a=\overline{a}\vee(a\wedge b), b=\overline{b}\vee(a\wedge b)$ and $\overline{a}\wedge \overline{b}=0$. The main purpose of this paper is to investigate prime ideals, minimal prime ideals and special ideals of a decomposable lattice. These are keys to understand the algebraic structure of decomposable lattices.Comment: 21 page

The size of 33-uniform hypergraphs with given matching number and codegree

Determine the size of $r$-graphs with given graph parameters is an interesting problem. Chv\'atal and Hanson (JCTB, 1976) gave a tight upper bound of the size of 2-graphs with restricted maximum degree and matching number; Khare (DM, 2014) studied the same problem for linear $3$-graphs with restricted matching number and maximum degree. In this paper, we give a tight upper bound of the size of $3$-graphs with bounded codegree and matching number.Comment: 16 page

CosRayMC: a global fitting method in studying the properties of the new sources of cosmic e±^{\pm} excesses

Recently PAMELA collaboration published the cosmic nuclei and electron spectra with high precision, together with the cosmic antiproton data updated, and the Fermi-LAT collaboration also updated the measurement of the total $e^+e^-$ spectrum to lower energies. In this paper we develop a Markov Chain Monte Carlo (MCMC) package {\it CosRayMC}, based on the GALPROP cosmic ray propagation model to study the implications of these new data. It is found that if only the background electrons and secondary positrons are considered, the fit is very bad with $\chi_{\rm red}^2 \approx 3.68$. Taking into account the extra $e^+e^-$ sources of pulsars or dark matter annihilation we can give much better fit to these data, with the minimum $\chi_{\rm red}^2 \approx 0.83$. This means the extra sources are necessary with a very high significance in order to fit the data. However, the data show little difference between pulsar and dark matter scenarios. Both the background and extra source parameters are well constrained with this MCMC method. Including the antiproton data, we further constrain the branching ratio of dark matter annihilation into quarks $B_q<0.5$ at $2\sigma$ confidence level. The possible systematical uncertainties of the present study are discussed.Comment: Published in Phys. Rev. D, 201