Parseval frames of exponentially localized magnetic Wannier functions

Motivated by the analysis of gapped periodic quantum systems in presence of a uniform magnetic field in dimension $d \le 3$, we study the possibility to construct spanning sets of exponentially localized (generalized) Wannier functions for the space of occupied states. When the magnetic flux per unit cell satisfies a certain rationality condition, by going to the momentum-space description one can model $m$ occupied energy bands by a real-analytic and $\mathbb Z^{d}$-periodic family $\{P({\bf k})\}_{{\bf k} \in \mathbb R^{d}}$ of orthogonal projections of rank $m$. A moving orthonormal basis of $\mathrm{Ran} P({\bf k})$ consisting of real-analytic and $\mathbb Z^d$-periodic Bloch vectors can be constructed if and only if the first Chern number(s) of $P$ vanish(es). Here we are mainly interested in the topologically obstructed case. First, by dropping the generating condition, we show how to algorithmically construct a collection of $m-1$ orthonormal, real-analytic, and periodic Bloch vectors. Second, by dropping the linear independence condition, we construct a Parseval frame of $m+1$ real-analytic and periodic Bloch vectors which generate $\mathrm{Ran} P({\bf k})$. Both algorithms are based on a two-step logarithm method which produces a moving orthonormal basis in the topologically trivial case. A moving Parseval frame of analytic, periodic Bloch vectors corresponds to a Parseval frame of exponentially localized composite Wannier functions. We extend this construction to the case of magnetic Hamiltonians with an irrational magnetic flux per unit cell and show how to produce Parseval frames of exponentially localized generalized Wannier functions also in this setting. Our results are illustrated in crystalline insulators modelled by $2d$ discrete Hofstadter-like Hamiltonians, but apply to certain continuous models of magnetic Schr\"{o}dinger operators as well.Comment: 40 pages. Improved exposition and minor corrections. Final version matches published paper on Commun. Math. Phy

Droplet: A New Denial-of-Service Attack on Low Power Wireless Sensor Networks

In this paper we present a new kind of Denial-of-Service attack against the PHY layer of low power wireless sensor networks. Overcoming the very limited range of jamming-based attacks, this attack can penetrate deep into a target network with high power efficiency. We term this the Droplet attack, as it attains enormous disruption by dropping small, payload-less frame headers to its victim's radio receiver, depriving the latter of bandwidth and sleep time. We demonstrate the Droplet attack's high damage rate to full duty-cycle receivers, and further show that a high frequency version of Droplet can even force nodes running on very low duty-cycle MAC protocols to drop most of their packets

Bounded Delay Scheduling with Packet Dependencies

A common situation occurring when dealing with multimedia traffic is having large data frames fragmented into smaller IP packets, and having these packets sent independently through the network. For real-time multimedia traffic, dropping even few packets of a frame may render the entire frame useless. Such traffic is usually modeled as having {\em inter-packet dependencies}. We study the problem of scheduling traffic with such dependencies, where each packet has a deadline by which it should arrive at its destination. Such deadlines are common for real-time multimedia applications, and are derived from stringent delay constraints posed by the application. The figure of merit in such environments is maximizing the system's {\em goodput}, namely, the number of frames successfully delivered. We study online algorithms for the problem of maximizing goodput of delay-bounded traffic with inter-packet dependencies, and use competitive analysis to evaluate their performance. We present competitive algorithms for the problem, as well as matching lower bounds that are tight up to a constant factor. We further present the results of a simulation study which further validates our algorithmic approach and shows that insights arising from our analysis are indeed manifested in practice

Energy ad a criterion for frame discarding and multiplexing efissiency

To design a STOM on the criterion of energies of each frame is one of the popUlar methods. In this each frames energy is calculated, a frame with lower energy is the best candidates among all users' speech frames. Dropping the frame with lmvest energy may degrade quality at its minimum as compared to the higher energy signals. This is also perceptually less important. Such frames of speech can be utilised to maximize the users on the link. This chapter talks about energy criterion as packet discarding for STDM design

Toward Digital, Critical, Participatory Action Research: Lessons From The #BarrioEdProj

The Education in our Barrios project, or #BarrioEdProj, is a digital critical participatory action research (D+CPAR) project that examines the interconnected remaking of public education and a New York City Latino core community in an era of racial capitalism. This article is a meditation on the ongoing development of #BarrioEdProj as an example of strategically coupling digital media with the theories and practices of critical participatory action research (CPAR). The author describes the project and the theoretical and political commitments that frame this project as a form of public and participatory science. The author then discusses some of the lessons that have been learned as the research group implemented the project and decided to move to a digital archiving model when our digital media design was initially ineffective. The author argues that rather than dropping digital media, engaged scholars must continue to explore the potentially transformative work that can come from carefully devised D+CPAR

Investigation on Seismic Performance of Cold-Formed Steel Portal Frames

A series of monotonous loading and hysteresis loading tests on cold-formed steel portal frames were conducted in this paper. The averaged ductility factor value of tested frames is 3.15 and the strength and stiffness degradation are not obvious during the test. The failure mode of frame is local buckling at column bases followed by local buckling at the top of columns, which lead to the dropping of frame’s load-carrying capacity. Then, the finite element model is developed and the analysis results match well with the test results. The research in this paper indicates that cold-formed steel portal frame has a good seismic performance

Frame rate required for speckle tracking echocardiography: A quantitative clinical study with open-source, vendor-independent software

Background Assessing left ventricular function with speckle tracking is useful in patient diagnosis but requires a temporal resolution that can follow myocardial motion. In this study we investigated the effect of different frame rates on the accuracy of speckle tracking results, highlighting the temporal resolution where reliable results can be obtained. Material and methods 27 patients were scanned at two different frame rates at their resting heart rate. From all acquired loops, lower temporal resolution image sequences were generated by dropping frames, decreasing the frame rate by up to 10-fold. Results Tissue velocities were estimated by automated speckle tracking. Above 40 frames/s the peak velocity was reliably measured. When frame rate was lower, the inter-frame interval containing the instant of highest velocity also contained lower velocities, and therefore the average velocity in that interval was an underestimate of the clinically desired instantaneous maximum velocity. Conclusions The higher the frame rate, the more accurately maximum velocities are identified by speckle tracking, until the frame rate drops below 40 frames/s, beyond which there is little increase in peak velocity. We provide in an online supplement the vendor-independent software we used for automatic speckle-tracked velocity assessment to help others working in this field