#nphs

Hybrid systems with non-polynomial components are widely used in modeling safety critical applications. Due to the complexity arisen from the non-polynomial expression, safety verification for such systems presents a grand challenge. In this paper, we present a new general approach to synthesizing rational invariants for safety verification of non-polynomial hybrid systems (NPHSs). Through system transformation and rational approximation, a NPHS is transformed into an over-approximate hybrid system in rational form. Then, for the over-approximate rational hybrid system, the proposed framework exploits a symbolic-numeric computation method to generate its exact rational invariants, which guarantees the safety property of the original NPHS. The test results show that the rational invariants yield better performances than those obtained from polynomial invariants.

Source: Oxford Journals

The following article was forwarded to us and originates from North Penn Highschool’s Special EDition Newsletter: Volume 2, Issue 2. This edition of the newsletter was sent out with the subject line, “What Could Happen If You Gave Someone A Chance?” and it features one of our most valuable employees, Mr. Frank D’Silva. Without Frank this office couldn’t possible run as smoothly as it does. His dedication is second to none, and we are honored to have the privilege of working with Frank each and everyday day. 

My name is Frank D'Silva, and I am an alumnus of the Class of 2010. I am fortunate to work at two jobs. I work full-time at D.i.D. which stands for Direct Image and Design Studio. D.i.D. is a healthcare advertising agency. I am an office assistant, and I have I worked there for 6 years. I make sure everything is wellstocked, I set up conference rooms for meetings, I take monthly inventory, and I coordinate the lunch club. 

I also work part-time at Giant Food Store as a service associate. When I was 16, I applied online and got the job! I am so glad I started working at 16. I liked my job, and it gave me responsibility. Giant is a good place to work, and I am still working there. It will be 9 years at the end of May!

During my Senior Year at NPHS, I was in the Career Work Study Program with Mrs. Wright and Mrs. Stadulis. I am so glad I participated in CWS. At the time, I thought I might be interested in culinary, but I wasn't sure. Mrs. Wright and Mrs. Stadulis set up experiences for me at a camera shop, grocery store kitchen, and a restaurant kitchen. I realized a kitchen was too fast-paced for me. D.i.D. had an opening for a new position -- an office assistant. My speech clinician, Mrs. Janoff, recommended me, so I interviewed for the position. They liked me and decided to give me a try. I worked at D.i.D. with a job coach as part of the Career Work Study Program. I stayed in NP post-12 for one year. During that year I worked at D.i.D. without a job coach, yet career work study checked back once a week to see how I was doing. I took my diploma in the summer of 2011. At that point, I was totally on my own -- no support from school! As time went on at DiD. I was given more responsibilities and my hours were increased. Today I work full-time with benefits. I am grateful to Mrs. Janoff, Mrs. Wright, Mrs. Stadulis, and Miss Jermain for giving me the jumpstart to D.i.D. I am grateful to D.i.D. for giving me the opportunity to work for them.

I am successful at my job because my job is important to me. I work hard and follow the rules. I always get to work on time. I like being independent. I don't have a driver's license, because I am afraid of other drivers and how they drive. I don't want them to tailgate and run into me. So, I walk to the train station and take the train everyday to work. Even when it is snowing or raining, I walk to the station.

My advice to students is that once you get the job, don't be nervous. If you don't understand something, just ask. I was so nervous when I got my job, but everyone enjoys working with me and I enjoy working with them.