The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary

We consider the dimer-monomer problem for the rectangular lattice. By mapping the problem into one of close-packed dimers on an extended lattice, we rederive the Tzeng-Wu solution for a single monomer on the boundary by evaluating a Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by identifying it as the product of the nonzero eigenvalues of the Kasteleyn matrix.Comment: 4 Pages to appear in the Physical Review E (2006

Factor PD-Clustering

Factorial clustering methods have been developed in recent years thanks to the improving of computational power. These methods perform a linear transformation of data and a clustering on transformed data optimizing a common criterion. Factorial PD-clustering is based on Probabilistic Distance clustering (PD-clustering). PD-clustering is an iterative, distribution free, probabilistic, clustering method. Factor PD-clustering make a linear transformation of original variables into a reduced number of orthogonal ones using a common criterion with PD-Clustering. It is demonstrated that Tucker 3 decomposition allows to obtain this transformation. Factor PD-clustering makes alternatively a Tucker 3 decomposition and a PD-clustering on transformed data until convergence. This method could significantly improve the algorithm performance and allows to work with large dataset, to improve the stability and the robustness of the method

Optimal synchronization of directed complex networks

We study optimal synchronization of networks of coupled phase oscillators. We extend previous theory for optimizing the synchronization properties of undirected networks to the important case of directed networks. We derive a generalized synchrony alignment function that encodes the interplay between network structure and the oscillators' natural frequencies and serves as an objective measure for the network's degree of synchronization. Using the generalized synchrony alignment function, we show that a network's synchronization properties can be systematically optimized. This framework also allows us to study the properties of synchrony-optimized networks, and in particular, investigate the role of directed network properties such as nodal in- and out-degrees. For instance, we find that in optimally rewired networks the heterogeneity of the in-degree distribution roughly matches the heterogeneity of the natural frequency distribution, but no such relationship emerges for out-degrees. We also observe that a network's synchronization properties are promoted by a strong correlation between the nodal in-degrees and the natural frequencies of oscillators, whereas the relationship between the nodal out-degrees and the natural frequencies has comparatively little effect. This result is supported by our theory, which indicates that synchronization is promoted by a strong alignment of the natural frequencies with the left singular vectors corresponding to the largest singular values of the Laplacian matrix

Anomalous suppression of the shot noise in a nanoelectromechanical system

In this paper we report a relaxation-induced suppression of the noise for a single level quantum dot coupled to an oscillator with incoherent dynamics in the sequential tunneling regime. It is shown that relaxation induces qualitative changes in the transport properties of the dot, depending on the strength of the electron-phonon coupling and on the applied voltage. In particular, critical thresholds in voltage and relaxation are found such that a suppression below 1/2 of the Fano factor is possible. Additionally, the current is either enhanced or suppressed by increasing relaxation, depending on bias being greater or smaller than the above threshold. These results exist for any strength of the electron-phonon coupling and are confirmed by a four states toy model.Comment: 7 pages, 7 eps figures, submitted to PRB; minor changes in the introductio

On the handling performance of a vehicle with different front-to-rear wheel torque distributions

The handling characteristic is a classical topic of vehicle dynamics. Usually, vehicle handling is studied through the analysis of the understeer coe�cient in quasi-steady-state maneuvers. In this paper, experimental tests are performed on an electric vehicle with four independent mo- tors, which is able to reproduce front-wheel-drive, rear-wheel-drive and all-wheel-drive (FWD, RWD and AWD, respectively) architectures. The handling characteristics of each architecture are inferred through classical and new concepts. More speci�cally, the study presents a pro- cedure to compute the longitudinal and lateral tire forces, which is based on a �rst estimate and a subsequent correction of the tire forces that guarantee the equilibrium. A yaw moment analysis is then performed to identify the contributions of the longitudinal and lateral forces. The results show a good agreement between the classical and new formulations of the un- dersteer coe�cient, and allow to infer a relationship between the understeer coe�cient and the yaw moment analysis. The handling characteristics for the considered maneuvers vary with the vehicle speed and front-to-rear wheel torque distribution. In particular, an apparently surprising result arises at low speed, where the RWD architecture is the most understeering con�guration. This outcome is discussed through the yaw moment analysis, highlighting the yaw moment caused by the longitudinal forces of the front tires, which is signi�cant for high values of lateral acceleration and steering angle

Theory of impedance networks: The two-point impedance and LC resonances

We present a formulation of the determination of the impedance between any two nodes in an impedance network. An impedance network is described by its Laplacian matrix L which has generally complex matrix elements. We show that by solving the equation L u_a = lambda_a u_a^* with orthonormal vectors u_a, the effective impedance between nodes p and q of the network is Z = Sum_a [u_{a,p} - u_{a,q}]^2/lambda_a where the summation is over all lambda_a not identically equal to zero and u_{a,p} is the p-th component of u_a. For networks consisting of inductances (L) and capacitances (C), the formulation leads to the occurrence of resonances at frequencies associated with the vanishing of lambda_a. This curious result suggests the possibility of practical applications to resonant circuits. Our formulation is illustrated by explicit examples.Comment: 21 pages, 3 figures; v4: typesetting corrected; v5: Eq. (63) correcte

FoldIndex©: a simple tool to predict whether a given protein sequence is intrinsically unfolded

Summary: An easy-to-use, versatile and freely available graphic web server, FoldIndex© is described: it predicts if a given protein sequence is intrinsically unfolded implementing the algorithm of Uversky and co-workers, which is based on the average residue hydrophobicity and net charge of the sequence. FoldIndex© has an error rate comparable to that of more sophisticated fold prediction methods. Sliding windows permit identification of large regions within a protein that possess folding propensities different from those of the whole protein. Availability: FoldIndex© can be accessed at http://bioportal.weizmann.ac.il/fldbin/findex Contact: [email protected] Supplementary information: http://www.weizmann.ac.il/sb/faculty_pages/Sussman/papers/suppl/Prilusky_200

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomorphic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of $N$ samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over- and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion formulas for resolution and overlapping kernel operators through the theory of Circulant Matrices and Rectangular Fourier Matrices. The case of band-limited functions on the Riemann sphere, with spins up to $J$, is also considered. The connection with the standard Euler angle picture, in terms of spherical harmonics, is established through a discrete Bargmann transform.Comment: 26 latex pages. Final version published in J. Fourier Anal. App