Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips

We determine the general structure of the partition function of the $q$-state Potts model in an external magnetic field, $Z(G,q,v,w)$ for arbitrary $q$, temperature variable $v$, and magnetic field variable $w$, on cyclic, M\"obius, and free strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices with width $L_y$ and arbitrarily great length $L_x$. For the cyclic case we prove that the partition function has the form $Z(\Lambda,L_y \times L_x,q,v,w)=\sum_{d=0}^{L_y} \tilde c^{(d)} Tr[(T_{Z,\Lambda,L_y,d})^m]$, where $\Lambda$ denotes the lattice type, $\tilde c^{(d)}$ are specified polynomials of degree $d$ in $q$, $T_{Z,\Lambda,L_y,d}$ is the corresponding transfer matrix, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for M\"obius strips, while only $T_{Z,\Lambda,L_y,d=0}$ appears for free strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$ and give illustrative examples. Explicit results for arbitrary $L_y$ are presented for $T_{Z,\Lambda,L_y,d}$ with $d=L_y$ and $d=L_y-1$. We find very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$. We also give results for self-dual cyclic strips of the square lattice.Comment: Reference added to a relevant paper by F. Y. W

Computational structures for robotic computations

The computational problem of inverse kinematics and inverse dynamics of robot manipulators by taking advantage of parallelism and pipelining architectures is discussed. For the computation of inverse kinematic position solution, a maximum pipelined CORDIC architecture has been designed based on a functional decomposition of the closed-form joint equations. For the inverse dynamics computation, an efficient p-fold parallel algorithm to overcome the recurrence problem of the Newton-Euler equations of motion to achieve the time lower bound of O(log sub 2 n) has also been developed

Globalization and Knowledge Spillover: International Direct Investment, Exports and Patents

This paper examines the impact of the three main channels of international trade on domestic innovation, namely outward direct investment, inward direct investment (IDI) and exports. The number of Triadic patents serves as a proxy for innovation. The data set contains 37 countries that are considered to be highly competitive in the world market, covering the period 1994 to 2005. The empirical results show that increased exports and outward direct investment are able to stimulate an increase in patent output. In contrast, IDI exhibits a negative relationship with domestic patents. The paper shows that the impact of IDI on domestic innovation is characterized by two forces, and the positive effect of cross-border mergers and acquisitions by foreigners is less than the negative effect of the remaining IDI.R&D;export;international direct investment;inward direct investment;negative binomial model;triadic patent;outward direct investment

Valproate and 4-methyloctanoic acid, an analogue of valproate, in animal models of epilepsy

Valproic acid (VPA) is a commonly used drug for the treatment of epilepsy, bipolar disorder and migraine, yet its mechanisms of action are unknown. The neuroprotective effect of VPA has been hypothesized to be secondary to inhibition of the cAMP/protein kinase A (PKA) pathway. Here, the result show that VPA (1mM) inhibited mossy fibre long-term potentiation induced (LTP) by application of high frequency stimulation in dentate gyrus. Furthermore, VPA (1mM) inhibited enhancement of mossy fibre responses induced by application of forskolin (50 μM), consistent with an effect on the PKA pathway. Using biochemical assays, it was further demonstrated that this was not due to a direct effect on PKA, but resulted from inhibition of adenylyl cyclase. The results further show using in vitro seizure models (Pentylenetetrazole model and low- Mg2+ model) that this mechanism cannot fully explain VPA’s anti-seizure effect, but rather, by modifying synaptic plasticity, it may be more important for VPA’s antiepileptogenic and neuroprotective action. VPA therefore has distinct mechanisms of action that contribute to its diverse biological activity. In hippocampi from epileptic rats (following pilocarpine-induced status epilepticus), but not in control tissue, VPA affects short-term plasticity, indicating that VPA may have specific effects in epileptic rather than control animals. Using in vitro seizure models (Pentylenetetrazole model and low-Mg2+ model) and an in vivo status epilepticus model (the perforant pathway stimulation model), 4- methyloctanoic acid is further established that it is a more potent antiepileptic drug than VPA and provides neuroprotective effects which are similar to VPA. Furthermore, 4- methyloctanoic acid (1mM) inhibited enhancement of mossy fibre responses induced by application of forskolin (50 μM), indicating that 4-methyloctanoic acid shares the same effect as VPA on modulation of PKA