Predictability and model selection in the context of ARCH models

Most of the methods used in the ARCH literature for selecting the appropriate model are based on evaluating the ability of the models to describe the data. An alternative model selection approach is examined based on the evaluation of the predictability of the models in terms of standardized prediction errors. Copyright © 2005 John Wiley & Sons, Ltd.     

Random Walks And The Colored Jones Function

It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagram, and another in terms of counting paths of intersecting chords. Electronic supplementary material to this article is available at and is accessible to authorized users. * S. G. was partially supported by an NSF and by an Israel-US BSF grant. † M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education.     

Approximation algorithms for scheduling problems with a modified total weighted tardiness objective

We study the approximability of minimum total weighted tardiness with a modified objective which includes an additive constant. This ensures the existence of a positive lower bound for the minimum value. Moreover the new objective has a natural interpretation in just-in-time production systems.     

Raman spectra of MgB2 at high pressure and topological electronic transition

Raman spectra of MgB₂ ceramic samples were measured as a function of pressure up to 32 GPa at room temperature. The spectrum at normal conditions contains a very broad peak at ∼590 cm⁻¹ related to the E _2g phonon mode. The frequency of this mode exhibits a strong linear dependence in the pressure region from 5 to 18 GPa, whereas, beyond this region, the slope of the pressure-induced frequency shift is reduced by about a factor of two. The pressure dependence of the phonon mode up to ∼5 GPa exhibits a change in the slope, as well as a “hysteresis” effect in the frequency vs. pressure behavior. These singularities in the E _2g mode behavior under pressure support the suggestion that MgB₂ may undergo a pressure-induced topological electronic transition.     

The dynamics of Rydberg electron wavepackets in NO

Rydberg electron wavepackets have been studied in molecular NO for a variety of rotational states of the ion core. Predominantly radial motion of the electron wavepacket is observed which is similar to that previously reported in atomic systems. Interference effects similar to those observed in unperturbed Rydberg series are evident and third and fourth order partial revivals are identified. Most interestingly, when the classical period of electronic motion is close to the classical period of rotation of the molecular ion, the molecular dynamics dominates the electronic dynamics.     

Synthesis and antitumor activity of new thiosemicarbazones of 2‐acetylimidazo[4,5‐b]pyridine

A number of thiosemicarbazones of 2‐acetyl‐imidazo[4,5‐b]pyridine were prepared in order to investigate their in vitro antineoplastic activities. Three compounds: (i) 2‐acetylimidazo[4,5‐b]pyridin‐4‐ sec ‐butyl‐3‐thiosemicarbazone [(A₇), NSC674098], (ii) 2‐acetylimidazo[4,5‐b]pyridin‐4‐tert‐butyl‐3‐thiosemi‐carbazone [(A₉), NSC674099], (iii) 2‐acetylimidazo[4,5‐b]pyridin‐4‐cyclohexyl‐3‐thiosemicarbozone [(A₁₁), NSC674101] showed remarkable activity against some of the cell lines tested. The Biological Evaluation Committee of N.C.I. determined that further secondary testing should be carried out (these compounds were tested against prostate cancer).     

2,4‐Diamino‐5‐(1‐naphthyl)‐3,5‐diaza‐1‐azoniaspiro[5.5]undeca‐1,3‐diene chloride

The title salt, C₁₈H₂₂N₅⁺·Cl^?, is a member of a new series of lipophilic 4,6‐di­amino spiro‐s‐triazines which are potent in­hib­itors of di­hydro­folate reductase. The protonated triazine ring deviates from planarity, whereas the cyclo­hexane ring adopts a chair conformation. A rather unusual hydrogen‐bonding scheme exists in the crystal. There is a centrosymmetric arrangement involving two amino groups and two triazine ring N atoms, with graph‐set R(8) and an N?N distance of 3.098 (3) Å, flanked by two additional R(8) systems, involving two amino groups, a triazine ring N atom and a Cl^? anion, with N?Cl distances in the range 3.179 (2)–3.278 (2) Å. Furthermore, the Cl^? anion, the protonated triazine ring N atom and an amino group form a hydrogen‐bonding system with graph‐set R(6).     

Phase-shifted Bragg microstructured optical fiber gratings utilizing infiltrated ferrofluids

Results are presented on the efficient spectral manipulation of uniform and chirped Bragg reflectors inscribed in microstructured optical fibers utilizing short lengths of ferrofluids infiltrated in their capillaries. The infiltrated ferrofluidic defects can generate either parasitic reflection notch features in uniform Bragg reflectors of up to 80% visibility and ~0.1 nm spectral shift or tunability of the bandwidth and strength reflection up to 100% when introduced into chirped gratings. Spectra are presented for different spatial positions and optical characteristics of the ferrofluidic section.     

A Simple Linear-Time Recognition Algorithm for Weakly Quasi-Threshold Graphs

Weakly quasi-threshold graphs form a proper subclass of the well-known class of cographs by restricting the join operation. In this paper we characterize weakly quasi-threshold graphs by a finite set of forbidden subgraphs: the class of weakly quasi-threshold graphs coincides with the class of {P ₄, co-(2P ₃)}-free graphs. Moreover we give the first linear-time algorithm to decide whether a given graph belongs to the class of weakly quasi-threshold graphs, improving the previously known running time. Based on the simplicity of our recognition algorithm, we can provide certificates of membership (a structure that characterizes weakly quasi-threshold graphs) or non-membership (forbidden induced subgraphs) in additional ${{\mathcal O}(n)}$ time. Furthermore we give a linear-time algorithm for finding the largest induced weakly quasi-threshold subgraph in a cograph.