RNN Controller for Lane-Keeping Systems with Robustness and Safety Verification

This paper proposes a Recurrent Neural Network (RNN) controller for lane-keeping systems, effectively handling model uncertainties and disturbances. First, quadratic constraints cover the nonlinearities brought by the RNN controller, and the linear fractional transformation method models the dynamics of system uncertainties. Second, we prove the robust stability of the lane-keeping system in the presence of uncertain vehicle speed using a linear matrix inequality. Then, we define a reachable set for the lane-keeping system. Finally, to confirm the safety of the lane-keeping system with tracking error bound, we formulate semidefinite programming to approximate the outer set of the reachable set. Numerical experiments demonstrate that this approach confirms the stabilizing RNN controller and validates the safety with an untrained dataset with untrained varying road curvatures.Comment: 7 pages, 6 figure

Uncertainty Quantification of Autoencoder-based Koopman Operator

This paper proposes a method for uncertainty quantification of an autoencoder-based Koopman operator. The main challenge of using the Koopman operator is to design the basis functions for lifting the state. To this end, this paper builds an autoencoder to automatically search the optimal lifting basis functions with a given loss function. We approximate the Koopman operator in a finite-dimensional space with the autoencoder, while the approximated Koopman has an approximation uncertainty. To resolve the problem, we compute a robust positively invariant set for the approximated Koopman operator to consider the approximation error. Then, the decoder of the autoencoder is analyzed by robustness certification against approximation error using the Lipschitz constant in the reconstruction phase. The forced Van der Pol model is used to show the validity of the proposed method. From the numerical simulation results, we confirmed that the trajectory of the true state stays in the uncertainty set centered by the reconstructed state.Comment: 6 pages, 3 figure

Statistical analysis of IMRT dosimetry quality assurance measurements for local delivery guideline

<p>Abstract</p> <p>Purpose</p> <p>To establish our institutional guideline for IMRT delivery, we statistically evaluated the results of dosimetry quality assurance (DQA) measurements and derived local confidence limits using the concept confidence limit of |mean|+1.96σ.</p> <p>Materials and methods</p> <p>From June 2006 to March 2009, 206 patients with head and neck cancer, prostate cancer, liver cancer, or brain tumor were treated using LINAC-based IMRT technique. In order to determine site specific DQA tolerances at a later stage, a hybrid plan with the same fluence maps as in the treatment plan was generated on CT images of a cylindrical phantom of acryl. Points of measurement using a 0.125 cm³ion-chamber were typically located in the region of high and uniform doses. The planar dose distributions perpendicular to the central axis were measured by using a diode array in solid water with all fields delivered, and assessed using gamma criteria of 3%/3 mm. The mean values and standard deviations were used to develop the local confidence and tolerance limits. The dose differences and gamma pass rates for the different treatment sites were also evaluated in terms of total monitor uints (MU), MU/cGy, and the number of PTV's pieces.</p> <p>Results</p> <p>The mean values and standard deviations of ion-chamber dosimetry differences between calculated and measured doses were -1.6 ± 1.2% for H&N cancer, -0.4 ± 1.2% for prostate and abdominal cancer, and -0.6 ± 1.5% for brain tumor. Most of measured doses (92.2%) agreed with the calculated doses within a tolerance limit of ±3% recommended in the literature. However, we found some systematic under-dosage for all treatment sites. The percentage of points passing the gamma criteria, averaged over all treatment sites was 97.3 ± 3.7%. The gamma pass rate and the agreement of ion-chamber dosimetry generally decreased with increasing the number of PTV's pieces, the degree of modulation (MU/cGy), and the total MU beyond 700. Our local confidence limits were comparable to those of AAPM TG 119 and ESTRO guidelines that were provided as a practical baseline for center-to-center commissioning comparison. Thus, our institutional confidence and action limits for IMRT delivery were set into the same levels of those guidelines.</p> <p>Discussion and Conclusions</p> <p>The systematic under-dosage were corrected by tuning up the MLC-related factors (dosimetric gap and transmission) in treatment planning system (TPS) and further by incorporating the tongue-and groove effect into TPS. Institutions that have performed IMRT DQA measurements over a certain period of time need to analyze their accrued DQA data. We confirmed the overall integrity of our IMRT system and established the IMRT delivery guideline during this procedure. Dosimetric corrections for the treatment plans outside of the action level can be suggested only with such rigorous DQA and statistical analysis.</p

Japans Special Procurement in the 1950s and the Cold War Structure

This article is a revised and translated version of the authors Korean article 1950-nyŏndae Ilbon ŭi tŭksu wa naengjŏn kujo, published in Ilbon pipŏng[Korean journal of Japanese studies] 22 (2020), with the permission of Sŏul Taehakkyo Ilbon Yŏnguso [Institute for Japanese Studies, Seoul National University].The practice of the special procurement of materials and logistical support from Japan, operated by the US that emerged after the Korean War, was an influential factor defining the Japanese economy through the 1950s. It facilitated the growth of Japanese economy by enabling the national annual acquisition of 800 million dollars of currency during the Korean War. To sustain economic growth, the Japanese government sought to secure new sources to replace the Korean War special procurement after the armistice. By utilizing US foreign aid sponsored offshore procurement, Japan was then able to acquire further procurement contracts amounting to 400 or 500 million dollars a year in the late 1950s. In addition to enabling the government to acquire foreign currency, special procurement also served as an opportunity to revive Japanese military industry and spearhead national economic influence in Southeast Asia. Japans economic gains from special procurement were rooted in its deep involvement in the US-led Cold War complex in East Asia. During the Korean War, Japan earned its special procurement income by undertaking the role of rear supply base. To secure further procurement of American dollars after the war, the government and business community responded to US initiatives and mobilized Japanese industrial productivity toward general procurement in support of US military forces, and participated in the US foreign aid strategy after the enforcement of the San Francisco Peace Treaty. Japan secured special economic benefits by actively committing to the US Cold War strategy for East Asia. Through these measures, the US fostered Japanese economic power as a rear supply base by providing the economic benefits of special procurement. Special procurement therefore embodied the shared interests of Japan and the US. On the other hand, special procurement also represented a crucial point at which the interests of Korea and Japan diverged. Not only because the Korean War special procurement occurred at the expense of immeasurable human and material loss within Korea, but also because the Korean reconstruction special procurement contributed to another form of Japans subjugation of the Korean economy.The translation and editing of this article were supported by the (Chae) Hakbong Changhakhoe [Hakbong Scholarship Foundation]

Note on combinatorial optimization with max-linear objective functions

AbstractWe consider combinatorial optimization problems with a feasible solution set S⊆{0,1}n specified by a system of linear constraints in 0–1 variables. Additionally, several cost functions c1,…,cp are given. The max-linear objective function is defined by f(x):=max{c1x,…,cpx: x∈S}; where cq:=(cq1,…,cqn) is for q=1,…,p an integer row vector in Rn.The problem of minimizing f(x) over S is called the max-linear combinatorial optimization (MLCO) problem.We will show that MLCO is NP-hard even for the simplest case of S⊆{0,1}n and p=2, and strongly NP-hard for general p. We discuss the relation to multi-criteria optimization and develop some bounds for MLCO

Segments in enumerating faces

We introduce the concept of a segment of a degenerate convex polytope specified by a system of linear constraints, and explain its importance in developing algorithms for enumerating the faces. Using segments, we describe an algorithm that enumerates all the faces, in time polynomial in their number. The role of segments in the unsolved problem of enumerating the extreme points of a convex polytope specified by a degenerate system of linear constraints, in time polynomial in the number of extreme points, is discussed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47929/1/10107_2005_Article_BF01585927.pd

DETERMINATION OF OPTIMAL LOCATIONS OF AMPHIBIAN ECO-DUCTS BY USING GENETIC ALGORITHMS: A CASE STUDY OF ODAESAN NATIONAL PARK IN KOREA

There are currently no systematic guidelines for placing the animal passes for wildlife to cross safely the human-made roads. This study presents a mathematical model that determines the optimal locations for amphibian eco-ducts by using a genetic algorithm. The study area is route no. 6 of Odaesan National Park in Korea, and the animals of focus are amphibians. The most crucial factor, the migration distance between amphibian road-kill sites and proposed eco-duct sites, was considered for determination of the optimal locations of amphibian eco-ducts. They were determined by calculating the minimum total distances associated with this factor near the road-kill sites. The model determined 69 optimal locations of ecoduct sites in eight sections of route no.6