4,727 research outputs found
Diffusion on an Ising chain with kinks
We count the number of histories between the two degenerate minimum energy configurations of the Ising model on a chain, as a function of the length n and the number d of kinks that appear above the critical temperature. This is equivalent to count permutations of length n avoiding certain subsequences depending on d. We give explicit generating functions and compute the asymptotics. The setting considered has a role when describing dynamics induced by quantum Hamiltonians with deconfined quasi-particles. (C) 2009 Elsevier B.V. All rights reserved
Wick's theorem for q-deformed boson operators
In this paper combinatorial aspects of normal ordering arbitrary words in the
creation and annihilation operators of the q-deformed boson are discussed. In
particular, it is shown how by introducing appropriate q-weights for the
associated ``Feynman diagrams'' the normally ordered form of a general
expression in the creation and annihilation operators can be written as a sum
over all q-weighted Feynman diagrams, representing Wick's theorem in the
present context.Comment: 9 page
Longitudinal LASSO: Jointly Learning Features and Temporal Contingency for Outcome Prediction
Longitudinal analysis is important in many disciplines, such as the study of
behavioral transitions in social science. Only very recently, feature selection
has drawn adequate attention in the context of longitudinal modeling. Standard
techniques, such as generalized estimating equations, have been modified to
select features by imposing sparsity-inducing regularizers. However, they do
not explicitly model how a dependent variable relies on features measured at
proximal time points. Recent graphical Granger modeling can select features in
lagged time points but ignores the temporal correlations within an individual's
repeated measurements. We propose an approach to automatically and
simultaneously determine both the relevant features and the relevant temporal
points that impact the current outcome of the dependent variable. Meanwhile,
the proposed model takes into account the non-{\em i.i.d} nature of the data by
estimating the within-individual correlations. This approach decomposes model
parameters into a summation of two components and imposes separate block-wise
LASSO penalties to each component when building a linear model in terms of the
past measurements of features. One component is used to select features
whereas the other is used to select temporal contingent points. An accelerated
gradient descent algorithm is developed to efficiently solve the related
optimization problem with detailed convergence analysis and asymptotic
analysis. Computational results on both synthetic and real world problems
demonstrate the superior performance of the proposed approach over existing
techniques.Comment: Proceedings of the 21th ACM SIGKDD International Conference on
Knowledge Discovery and Data Mining. ACM, 201
Multi-core job submission and grid resource scheduling for ATLAS AthenaMP
AthenaMP is the multi-core implementation of the ATLAS software framework and allows the efficient sharing of memory pages between multiple threads of execution. This has now been validated for production and delivers a significant reduction on the overall application memory footprint with negligible CPU overhead. Before AthenaMP can be routinely run on the LHC Computing Grid it must be determined how the computing resources available to ATLAS can best exploit the notable improvements delivered by switching to this multi-process model. A study into the effectiveness and scalability of AthenaMP in a production environment will be presented. Best practices for configuring the main LRMS implementations currently used by grid sites will be identified in the context of multi-core scheduling optimisation
Matrix permanent and quantum entanglement of permutation invariant states
We point out that a geometric measure of quantum entanglement is related to
the matrix permanent when restricted to permutation invariant states. This
connection allows us to interpret the permanent as an angle between vectors. By
employing a recently introduced permanent inequality by Carlen, Loss and Lieb,
we can prove explicit formulas of the geometric measure for permutation
invariant basis states in a simple way.Comment: 10 page
A general algorithm for manipulating non-linear and linear entanglement witnesses by using exact convex optimization
A generic algorithm is developed to reduce the problem of obtaining linear
and nonlinear entanglement witnesses of a given quantum system, to convex
optimization problem. This approach is completely general and can be applied
for the entanglement detection of any N-partite quantum system. For this
purpose, a map from convex space of separable density matrices to a convex
region called feasible region is defined, where by using exact convex
optimization method, the linear entanglement witnesses can be obtained from
polygonal shape feasible regions, while for curved shape feasible regions,
envelope of the family of linear entanglement witnesses can be considered as
nonlinear entanglement witnesses. This method proposes a new methodological
framework within which most of previous EWs can be studied. To conclude and in
order to demonstrate the capability of the proposed approach, besides providing
some nonlinear witnesses for entanglement detection of density matrices in
unextendible product bases, W-states, and GHZ with W-states, some further
examples of three qubits systems and their classification and entanglement
detection are included. Also it is explained how one can manipulate most of the
non-decomposable linear and nonlinear three qubits entanglement witnesses
appearing in some of the papers published by us and other authors, by the
method proposed in this paper. Keywords: non-linear and linear entanglement
witnesses, convex optimization. PACS number(s): 03.67.Mn, 03.65.UdComment: 37 page
Equitability revisited: why the âequitable threat scoreâ is not equitable
In the forecasting of binary events, verification measures that are âequitableâ were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weights are independent of the entries in the table, apart from the base rate. The authors demonstrate that the widely used âequitable threat scoreâ (ETS), as well as numerous others, satisfies neither of these requirements and only satisfies the first requirement in the limit of an infinite sample size. Such measures are referred to as âasymptotically equitable.â In the case of ETS, the expected score of a random forecasting system is always positive and only falls below 0.01 when the number of samples is greater than around 30. Two other asymptotically equitable measures are the odds ratio skill score and the symmetric extreme dependency score, which are more strongly inequitable than ETS, particularly for rare events; for example, when the base rate is 2% and the sample size is 1000, random but unbiased forecasting systems yield an expected score of around â0.5, reducing in magnitude to â0.01 or smaller only for sample sizes exceeding 25 000. This presents a problem since these nonlinear measures have other desirable properties, in particular being reliable indicators of skill for rare events (provided that the sample size is large enough). A potential way to reconcile these properties with equitability is to recognize that Gandin and Murphyâs two requirements are independent, and the second can be safely discarded without losing the key advantages of equitability that are embodied in the first. This enables inequitable and asymptotically equitable measures to be scaled to make them equitable, while retaining their nonlinearity and other properties such as being reliable indicators of skill for rare events. It also opens up the possibility of designing new equitable verification measures
- âŠ