Transparent In-Circuit Assertions for FPGAs

Commonly used in software design, assertions are statements placed into a design to ensure that its behaviour matches that expected by a designer. Although assertions apply equally to hardware design, they are typically supported only for logic simulation, and discarded prior to physical implementation. We propose a new HDL-agnostic language for describing latency-insensitive assertions and novel methods to add such assertions transparently to an already placed-and-routed circuit without affecting the existing design. We also describe how this language and associated methods can be used to implement semi-transparent exception handling. The key to our work is that by treating hardware assertions and exceptions as being oblivious or less sensitive to latency, assertion logic need only use spare FPGA resources. We use network-flow techniques to route necessary signals to assertions via spare flip-flops, eliminating any performance degradation, even on large designs (92% of slices in one test). Experimental evaluation shows zero impact on critical-path delay, even on large benchmarks operating above 200MHz, at the cost of a small power penalty

The range of the tangential Cauchy-Riemann system on a CR embedded manifold

We prove that every compact, pseudoconvex, orientable, CR manifold of \C^n, bounds a complex manifold in the $C^\infty$ sense. In particular, the tangential Cauchy-Riemann system has closed range

ANALYSIS OF STRATEGY USED IN TAEKWONDO COMPETITION

The purpose of this study was to investigate the strategy used in the Taekwondo competition. A total of 21 matches, consisting of 1598 offensive and defensive events, were video taped. Competition strategy, based on frame-by-frame video analysis, was employed to classify the athlete’s motion. Offensive and defensive kicking technique, in order of priority, was roundhouse kick (72.7%), double roundhouse kick (11.0%), back kick (8.0%), cut down kick (3.3%), pushing kick (2.2%), spinning hook kick (1.9%), side kick (0.8%), and hook kick (0.2%). The methodology employed in this study and the data reported may be useful to coaches and athletes interested in gaining insight on the strategy of patterns used in Taekwondo competition

A Unified Systolic Array for Adaptive Beamforming

We present a new algorithm and systolic array for adaptive beamforming. Our approach improves on McWhirter\u27s pioneering work in two respects. First, our algorithm uses only orthogonal transformations and this should have better numerical properties. Second, the algorithms can be implemented on one single pxp triangular array of programmable processors that offers a throughput of one residual element per cycle

A Novel MVDR Beamforming Algorithm

We propose a novel algorithm and architecture for minimum variance distortions less response (MVDR) beamforming. Our approach extracts the least squares residual element directly, and requires only one systolic array for the many look directions

The Vlasov--Poisson--Landau system in the weakly collisional regime

Consider the Vlasov--Poisson--Landau system with Coulomb potential in the weakly collisional regime on a $3$-torus, i.e. $$\begin{aligned} \partial_t F(t,x,v) + v_i \partial_{x_i} F(t,x,v) + E_i(t,x) \partial_{v_i} F(t,x,v) = \nu Q(F,F)(t,x,v),\\ E(t,x) = \nabla \Delta^{-1} (\int_{\mathbb R^3} F(t,x,v)\, \mathrm{d} v - \frac{1}{(2\pi)^3}\int_{\mathbb T^3} \int_{\mathbb R^3} F(t,x,v)\, \mathrm{d} v \, \mathrm{d} x), \end{aligned}$$ with $\nu\ll 1$. We prove that for $\epsilon>0$ sufficiently small (but independent of $\nu$), initial data which are $O(\epsilon \nu^{1/3})$-Sobolev space perturbations from the global Maxwellians lead to global-in-time solutions which converge to the global Maxwellians as $t\to \infty$. The solutions exhibit uniform-in-$\nu$ Landau damping and enhanced dissipation. Our main result is analogous to an earlier result of Bedrossian for the Vlasov--Poisson--Fokker--Planck equation with the same threshold. However, unlike in the Fokker--Planck case, the linear operator cannot be inverted explicitly due to the complexity of the Landau collision operator. For this reason, we develop an energy-based framework, which combines Guo's weighted energy method with the hypocoercive energy method and the commuting vector field method. The proof also relies on pointwise resolvent estimates for the linearized density equation.Comment: 78 Pages. Comments welcome