Related papers: Geometric Programming for 3D Circuits
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
Parametric Computer-aided design (CAD) enables the creation of reusable models by integrating variables into geometric properties, facilitating customization without a complete redesign. However, creating parametric designs in…
Grid layouts are used by designers to spatially organise user interfaces when sketching and wireframing. However, their design is largely time consuming manual work. This is challenging due to combinatorial explosion and complex objectives,…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
Enhancement of the number and array density of nozzles within an inkjet head chip is one of the keys to raise the printing speed and printing resolutions. However, traditional 2D architecture of driving circuits can not meet the requirement…
We challenge the current thinking and approach to the design of photonic integrated circuits (PICs) for applications in communications, quantum information and sensing. The standard PICs are based on directional couplers, that provide a…
Digital Geometry software should reflect the generality of the underlying mathe- matics: mapping the latter to the former requires genericity. By designing generic solutions, one can effectively reuse digital geometry data structures and…
As experimental quantum information processing (QIP) rapidly advances, an emerging challenge is to design a scalable architecture that combines various quantum elements into a complex device without compromising their performance. In…
This paper presents a novel, high-performance, graphical processing unit-based algorithm for efficiently solving two-dimensional linear programs in batches. The domain of two-dimensional linear programs is particularly useful due to the…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
Modern multi-core systems have a large number of design parameters, most of which are discrete-valued, and this number is likely to keep increasing as chip complexity rises. Further, the accurate evaluation of a potential design choice is…
Measurements of microscale surface patterns are essential for process and quality control in industries across semiconductors, micro-machining, and biomedicines. However, the development of miniaturized and intelligent profiling systems…
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…
We express the finite 3D Dimer partition function as a linear combination of determinants of oriented adjacency matrices, and the finite 3D Ising partition sum as a linear combination of products over aperiodic closed walks. The methodology…
Three dimensional (3D) structures composed of planar surfaces can be build out of accessible materials using easier fabrication technique with shorter fabrication time. To better design 3D structures with planar surfaces, realistic models…
Network-on-Chips (NoCs) have been widely employed in the design of multiprocessor system-on-chips (MPSoCs) as a scalable communication solution. NoCs enable communications between on-chip Intellectual Property (IP) cores and allow those…
We propose a new geometric method of IR factorization in sector decomposition. The problem is converted into a set of problems in convex geometry. The latter problems are solved using algorithms in combinatorial geometry. This method…
There is increasing demand for automated systems that can fabricate 3D structures. Robotic spatial extrusion has become an attractive alternative to traditional layer-based 3D printing due to a manipulator's flexibility to print large,…
ReRAM-based in-memory computing (IMC) architectures are promising candidates for energy-efficient matrix-vector multiplication. While scaling the size of ReRAM arrays allows for the amortization of power-hungry peripheral circuits like DACs…
In the field of nonlinear mechanics, many challenging problems (e.g. plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity…