TY - JOUR
AU - González, J.
AU - de Vladar, Harold
AU - Rebolledo, Morella
ID - 4240
JF - Acta Científica Venezolana
TI - New Late–Intensification Schedules for Cancer Treatments
VL - 54
ER -
TY - THES
AB - Methods for the formal specification and verification of systems are indispensible for the development of complex yet correct systems. In formal verification, the designer describes the system in a modeling language with a well-defined semantics, and this system description is analyzed against a set of correctness requirements. Model checking is an algorithmic technique to check that a system description indeed satisfies correctness requirements given as logical specifications. While successful in hardware verification, the potential for model checking for software and embedded systems has not yet been realized. This is because traditional model checking focuses on systems modeled as finite state-transition graphs. While a natural model for hardware (especially synchronous hardware), state-transition graphs often do not capture software and embedded systems at an appropriate level of granularity. This dissertation considers two orthogonal extensions to finite state-transition graphs making model checking techniques applicable to both a wider class of systems and a wider class of properties.
The first direction is an extension to infinite-state structures finitely represented using constraints and operations on constraints. Infinite state arises when we wish to model variables with unbounded range (e.g., integers), or data structures, or real time. We provide a uniform framework of symbolic region algebras to study model checking of infinite-state systems. We also provide sufficient language-independent termination conditions for symbolic model checking algorithms on infinite state systems.
The second direction supplements verification with game theoretic reasoning. Games are natural models for interactions between components. We study game theoretic behavior with winning conditions given by temporal logic objectives both in the deterministic and in the probabilistic context. For deterministic games, we provide an extremal model characterization of fixpoint algorithms that link solutions of verification problems to solutions for games. For probabilistic games we study fixpoint characterization of winning probabilities for games with omega-regular winning objectives, and construct (epsilon-)optimal winning strategies.
AU - Majumdar, Ritankar
ID - 4416
TI - Symbolic algorithms for verification and control
ER -
TY - THES
AB - Giotto provides a time-triggered programmer’s model for the implementation of embedded control systems with hard real-time constraints. Giotto’s precise semantics and predictabil- ity make it suitable for safety-critical applications.
Giotto is based around the idea that time-triggered task invocation together with time-triggered mode switching can form a useful programming model for real-time systems. To substantiate this claim, we describe the use of Giotto to refactor the software of a small, autonomous helicopter. The ease with which Giotto expresses the existing software provides evidence that Giotto is an appropriate programming language for control systems.
Since Giotto is a real-time programming language, ensuring that Giotto programs meet their deadlines is crucial. To study precedence-constrained Giotto scheduling, we first examine single-mode, single-processor scheduling. We extend to an infinite, periodic setting the classical problem of meeting deadlines for a set of tasks with release times, deadlines, precedence constraints, and preemption. We then develop an algorithm for scheduling Giotto programs on a single processor by representing Giotto programs as instances of the extended scheduling problem.
Next, we study multi-mode, single-processor Giotto scheduling. This problem is different from classical scheduling problems, since in our precedence-constrained approach, the deadlines of tasks may vary depending on the mode switching behavior of the program. We present conditional scheduling models which capture this varying-deadline behavior. We develop polynomial-time algorithms for some conditional scheduling models, and prove oth- ers to be computationally hard. We show how to represent multi-mode Giotto programs as instances of the model, resulting in an algorithm for scheduling multi-mode Giotto programs on a single processor.
Finally, we show that the problem of scheduling Giotto programs for multiple net- worked processors is strongly NP-hard.
AU - Horowitz, Benjamin
ID - 4425
TI - Giotto: A time-triggered language for embedded programming
ER -
TY - JOUR
AU - Kaloshin, Vadim
ID - 8519
IS - 3
JF - Inventiones mathematicae
KW - General Mathematics
SN - 0020-9910
TI - The existential Hilbert 16-th problem and an estimate for cyclicity of elementary polycycles
VL - 151
ER -
TY - JOUR
AB - Let k⩾5 be an integer, and let x⩾1 be an arbitrary real number. We derive a bound[Formula presented] for the number of positive integers less than or equal to x which can be represented as a sum of two non-negative coprime kth powers, in essentially more than one way.
AU - Timothy Browning
ID - 204
IS - 2
JF - Journal of Number Theory
TI - Equal Sums of Two kth Powers
VL - 96
ER -
TY - CHAP
AU - Lieb, Élliott H
AU - Solovej, Jan P
AU - Robert Seiringer
AU - Yngvason, Jakob
ID - 2338
T2 - Current Developments in Mathematics, 2001
TI - The ground state of the Bose gas
ER -
TY - CONF
AU - Robert Seiringer
ED - Weder, Richardo
ED - Exner, Pavel
ED - Grébert, Benoit
ID - 2339
TI - Symmetry breaking in a model of a rotating Bose gas
VL - 307
ER -
TY - JOUR
AB - The Bose-Einstein condensation (BEC) of the ground state of bosonic atoms in a trap was discussed. The BEC was proved for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schrodinger equation. The BEC was 100% into the state which minimized the Gross-Pitaevskii energy functional. The analysis also included rigorous proof of BEC in a physically realistic, continuum model.
AU - Lieb, Élliott H
AU - Robert Seiringer
ID - 2349
IS - 17
JF - Physical Review Letters
TI - Proof of Bose-Einstein condensation for dilute trapped gases
VL - 88
ER -
TY - JOUR
AB - Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge Z and in presence of the quantized radiation field. We consider the case of small coupling constant α, but fixed Zα and ultraviolet cut-off Λ. We prove that after renormalizing the mass the binding energy has, to leading order in α, a finite limit as Λ goes to infinity; i.e., the cut-off can be removed. The expression for the ground state energy shift thus obtained agrees with Bethe's formula for small values of Zα, but shows a different behavior for bigger values.
AU - Hainzl, Christian
AU - Robert Seiringer
ID - 2350
IS - 5
JF - Advances in Theoretical and Mathematical Physics
TI - Mass renormalization and energy level shift in non-relativistic QED
VL - 6
ER -
TY - JOUR
AB - We study the Gross-Pitaevskii functional for a rotating two-dimensional Bose gas in a trap. We prove that there is a breaking of the rotational symmetry in the ground state; more precisely, for any value of the angular velocity and for large enough values of the interaction strength, the ground state of the functional is not an eigenfunction of the angular momentum. This has interesting consequences on the Bose gas with spin; in particular, the ground state energy depends non-trivially on the number of spin components, and the different components do not have the same wave function. For the special case of a harmonic trap potential, we give explicit upper and lower bounds on the critical coupling constant for symmetry breaking.
AU - Robert Seiringer
ID - 2351
IS - 3
JF - Communications in Mathematical Physics
TI - Gross-Pitaevskii theory of the rotating Bose gas
VL - 229
ER -