Supersymmetry and the LHC Inverse Problem

Given experimental evidence at the LHC for physics beyond the standard model, how can we determine the nature of the underlying theory? We initiate an approach to studying the "inverse map" from the space of LHC signatures to the parameter space of theoretical models within the context of low-energy supersymmetry, using 1808 LHC observables including essentially all those suggested in the literature and a 15 dimensional parametrization of the supersymmetric standard model. We show that the inverse map of a point in signature space consists of a number of isolated islands in parameter space, indicating the existence of "degeneracies"--qualitatively different models with the same LHC signatures. The degeneracies have simple physical characterizations, largely reflecting discrete ambiguities in electroweak-ino spectrum, accompanied by small adjustments for the remaining soft parameters. The number of degeneracies falls in the range 1<d<100, depending on whether or not sleptons are copiously produced in cascade decays. This number is large enough to represent a clear challenge but small enough to encourage looking for new observables that can further break the degeneracies and determine at the LHC most of the SUSY physics we care about. Degeneracies occur because signatures are not independent, and our approach allows testing of any new signature for its independence. Our methods can also be applied to any other theory of physics beyond the standard model, allowing one to study how model footprints differ in signature space and to test ways of distinguishing qualitatively different possibilities for new physics at the LHC.Comment: 55 pages, 30 figure

Definability of linear equation systems over groups and rings

Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and rings from the viewpoint of logical (inter-)definability. All problems that we consider are decidable in polynomial time, but not expressible in fixed-point logic with counting. They also provide natural candidates for a separation of polynomial time from rank logics, which extend fixed-point logics by operators for determining the rank of definable matrices and which are sufficient for solvability problems over fields. Based on the structure theory of finite rings, we establish logical reductions among various solvability problems. Our results indicate that all solvability problems for linear equation systems that separate fixed-point logic with counting from PTIME can be reduced to solvability over commutative rings. Moreover, we prove closure properties for classes of queries that reduce to solvability over rings, which provides normal forms for logics extended with solvability operators. We conclude by studying the extent to which fixed-point logic with counting can express problems in linear algebra over finite commutative rings, generalising known results on the logical definability of linear-algebraic problems over finite fields

Remarks on the notion of quantum integrability

We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different integrability classes. We end by highlighting some of the expected physical properties associated to models fulfilling the proposed criteria.Comment: 22 pages, no figures, Proceedings of Statphys 2

Compact Markov-modulated models for multiclass trace fitting

Markov-modulated Poisson processes (MMPPs) are stochastic models for fitting empirical traces for simulation, workload characterization and queueing analysis purposes. In this paper, we develop the first counting process fitting algorithm for the marked MMPP (M3PP), a generalization of the MMPP for modeling traces with events of multiple types. We initially explain how to fit two-state M3PPs to empirical traces of counts. We then propose a novel form of composition, called interposition, which enables the approximate superposition of several two-state M3PPs without incurring into state space explosion. Compared to exact superposition, where the state space grows exponentially in the number of composed processes, in interposition the state space grows linearly in the number of composed M3PPs. Experimental results indicate that the proposed interposition methodology provides accurate results against artificial and real-world traces, with a significantly smaller state space than superposed processes