Faster algorithms for computing longest common increasing subsequences

We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For two sequences of lengths n and m, where m?n, we present an algorithm with an output-dependent expected running time of and O(m) space, where ? is the length of an LCIS, σ is the size of the alphabet, and Sort is the time to sort each input sequence. For k?3 length-n sequences we present an algorithm which improves the previous best bound by more than a factor k for many inputs. In both cases, our algorithms are conceptually quite simple but rely on existing sophisticated data structures. Finally, we introduce the problem of longest common weakly-increasing (or non-decreasing) subsequences (LCWIS), for which we present an -time algorithm for the 3-letter alphabet case. For the extensively studied longest common subsequence problem, comparable speedups have not been achieved for small alphabets.     

Including inputs and control within equation-free architectures for complex systems

The increasing ubiquity of complex systems that require control is a challenge for existing methodologies in characterization and controller design when the system is high-dimensional, nonlinear, and without physics-based governing equations. We review standard model reduction techniques such as Proper Orthogonal Decomposition (POD) with Galerkin projection and Balanced POD (BPOD). Further, we discuss the link between these equation-based methods and recently developed equation-free methods such as the Dynamic Mode Decomposition and Koopman operator theory. These data-driven methods can mitigate the challenge of not having a well-characterized set of governing equations. We illustrate that this equation-free approach that is being applied to measurement data from complex systems can be extended to include inputs and control. Three specific research examples are presented that extend current equation-free architectures toward the characterization and control of complex systems. These examples motivate a potentially revolutionary shift in the characterization of complex systems and subsequent design of objective-based controllers for data-driven models.     

Aromatic substitution by n-arylhydroxylamines—I : Formation of 8-amino-5,8′-iminobis(6-methoxyquinoline) by an intermolecular aromatic nitrene insertion reaction

Thermolysis of 8-hydroxylamino-6-methoxyquinoline at 65° in methanol gave 8-amino-5,8′-iminobis(6-methoxyquinoline), the same product being formed by thermolysis of 8-azido-6-methoxyquinoline as well as by deoxygenation of 6-methoxy-8-nitroquinoline with triethylphosphite in the presence of 8-amino-6-methoxyquinoline. Solvent effects were also consistent with the involvement of a nitrenoid species in these intermolecular aromatic substitutons. 8-Hydroxylaminoquinoline behaved in an analogous fashion but no iminobis compound was obtained from the corresponding 6-hydroxylaminoquinoline, indicating an internal interaction of the ring N atom with the 8-hydroxylamino function. Thermolysis of 8-hydroxylamino-6-methoxyquinoline in the presence of amines gave rise to o-diamines reconcilable with a nitrene intermediate.     

Synthesis of Methylene‐Bridged Biscarbazole Alkaloids by using an Ullmann‐type Coupling: First Total Synthesis of Murrastifoline‐C and Murrafoline‐E

We describe the total synthesis of methylene‐bridged biscarbazole alkaloids by using a late‐stage Ullmann‐type coupling of fully functionalised carbazole subunits. The carbazole derivatives were synthesised via a sequence of palladium(0)‐ and palladium(II)‐catalysed coupling reactions. Our approach has provided bismurrayafoline‐A, bismurrayafolinol, chrestifolines B–D, and the first total synthesis of murrastifoline‐C and murrafoline‐E.     

Sum-frequency generation of acetate adsorption on Au and Pt surfaces: molecular structure effects

The reversible adsorption of acetate on polycrystalline Au and Pt surfaces was investigated with broadband sum-frequency generation (SFG) and cyclic voltammetry. Specifically adsorbed acetate as well as coadsorbed sulfuric acid anions are observed for the first time with SFG and give rise to dramatically different SFG intensities on Au and Pt surfaces. While similar coverages of acetate adlayers on Au and Pt surfaces are well established by previous studies, an identification of the interfacial molecular structure has been elusive. However, we have applied the high sensitivity of SFG for interfacial polar ordering to identify different acetate structures at Au and Pt surfaces in contact with HClO(4) and H(2)SO(4) electrolytes. Acetate competes with the formation of surface oxides and shifts the oxidation threshold of both Au and Pt electrodes anodically. Effects of the supporting electrolyte on the formation of acetate adlayers are revealed by comparing SFG spectra in HClO(4) and H(2)SO(4) solutions: Sulfuric acid anions modify the potential-dependent acetate adsorption, compete with adsorbed acetate on Au and coadsorb with acetate on Pt surfaces.     

Characterizing bifurcations and chaos in multiwavelength lasers with intensity-dependent loss and saturable homogeneous gain

We consider the nonlinear dynamics of multiwavelength laser cavities with saturable transmitter and saturating homogeneous gain using a simple and general discrete model. Saturable transmitter is an intensity dependent loss in which the transmittance decreases when the incident optical power increases. We determine the condition under which the saturable transmitter will generate behaviors such as stable steady-state lasing states, periodic lasing states, and chaotic lasing states. Indeed, for sufficiently large power, steady-state operation is first destabilized through a Hopf bifurcation which generates periodic lasing solutions. This is followed by a sequence of period doubling bifurcations to chaotic lasing. The bifurcation structure leading to chaos is characterized by three key methods of dynamical systems: a Feigenbaum series, the calculation of Lyapunov exponents and the computation of the correlation dimension of the system. We found that even single wavelength operation can exhibit complex nonlinear dynamics if the loss element is a saturable transmitter.     

Sparse chip equalizer for DS-CDMA downlink receivers

We present a low complexity sparse chip equalization scheme for DS-CDMA downlink receivers in which only a small number of filter taps are selected to be non-zero, thereby reducing the computational complexity significantly. Low complexity algorithms for selecting the timings and complex amplitudes of the sparse equalizer taps are proposed. The excellent performance achieved by this scheme combined with its low complexity makes it an attractive choice for the DS-CDMA based cellular downlink receivers.     

Dynamics and stability of a new class of periodic solutions of the optical parametric oscillator

The stability and dynamics of a new class of periodic solutions is investigated when a degenerate optical parametric oscillator system is forced by an external pumping field with a periodic spatial profile modeled by Jacobi elliptic functions. Both sinusoidal behavior as well as localized hyperbolic (front and pulse) behavior can be considered in this model. The stability and bifurcation behaviors of these transverse electromagnetic structures are studied numerically. The periodic solutions are shown to be stabilized by the nonlinear parametric interaction between the pump and signal fields interacting with the cavity diffraction, attenuation, and periodic external pumping. Specifically, sinusoidal solutions result in robust and stable configurations while well-separated and more localized field structures often undergo bifurcation to new steady-state solutions having the same period as the external forcing. Extensive numerical simulations and studies of the solutions are provided.     

Theory and simulation of passive modelocking dynamics using a long-period fiber grating

A novel modelocking technique is presented in which the intensity-dependent mode-coupling dynamics of a long-period fiber grating is used to achieve modelocking in a passive optical fiber laser. By an appropriate choice of the grating period, a resonant coupling occurs between co-propagating core and cladding modes, causing the low-intensity wings of the pulse to be transferred to the cladding mode and be attenuated. In contrast, the higher intensity peaks of a pulse are detuned from resonance by the nonlinearity and remain largely unaffected. Numerical studies of this pulse-shaping mechanism show that the laser produces stable mode-locked soliton-like pulses which are limited in bandwidth by the smaller of either the grating transmission bandwidth or amplifier bandwidth.