Desktop Sharing Portal

Desktop sharing technologies have existed since the late 80s. It is often used in scenarios where collaborative computing is beneficial to participants in the shared environment by the control of the more knowledgeable party. But the steps required in establishing a session is often cumbersome to many. Selection of a sharing method, obtaining sharing target’s network address, sharing tool’s desired ports, and firewall issues are major hurdles for a typical non-IT user. In this project, I have constructed a web-portal that helps collaborators to easily locate each other and initialize sharing sessions. The portal that I developed enables collaborated sessions to start as easily as browsing to a URL of the sharing service provider, with no need to download or follow installation instructions on either party’s end. In addition, I have added video conferencing and audio streaming capability to bring better collaborative and multimedia experience

Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page

Cerebellum to motor cortex paired associative stimulation induces bidirectional STDP-like plasticity in human motor cortex

The cerebellum is crucially important for motor control and adaptation. Recent non-invasive brain stimulation studies have indicated the possibility to alter the excitability of the cerebellum and its projections to the contralateral motor cortex, with behavioral consequences on motor control and adaptation. Here we sought to induce bidirectional spike-timing dependent plasticity (STDP)-like modifications of motor cortex (M1) excitability by application of paired associative stimulation (PAS) in healthy subjects. Conditioning stimulation over the right lateral cerebellum (CB) preceded focal transcranial magnetic stimulation (TMS) of the left M1 hand area at an interstimulus interval of 2 ms (CB→M1 PAS(2 ms)), 6 ms (CB→M1 PAS(6 ms)) or 10 ms (CB→M1 PAS(10 ms)) or randomly alternating intervals of 2 and 10 ms (CB→M1 PAS(Control)). Effects of PAS on M1 excitability were assessed by the motor-evoked potential (MEP) amplitude, short-interval intracortical inhibition (SICI), intracortical facilitation (ICF) and cerebellar-motor cortex inhibition (CBI) in the first dorsal interosseous muscle of the right hand. CB→M1 PAS(2 ms) resulted in MEP potentiation, CB→M1 PAS(6 ms) and CB→M1 PAS(10 ms) in MEP depression, and CB→M1 PAS(Control) in no change. The MEP changes lasted for 30-60 min after PAS. SICI and CBI decreased non-specifically after all PAS protocols, while ICF remained unaltered. The physiological mechanisms underlying these MEP changes are carefully discussed. Findings support the notion of bidirectional STDP-like plasticity in M1 mediated by associative stimulation of the cerebello-dentato-thalamo-cortical pathway and M1. Future studies may investigate the behavioral significance of this plasticity