Eisenstein--Jacobi (EJ) networks are degree-six quotient-lattice interconnection networks. For a generator $\alpha=a+b\rho$, let $N=a^2+ab+b^2$ and $d=\gcd(a,b)$. If $d=1$, the three natural unit directions already give three edge-disjoint Hamiltonian cycles. If $d>1$, each unit direction splits into $d$ cycles and the EDHC problem becomes a cycle-splicing problem. Existing non-coprime EJ decompositions prove existence by using a rectangular rep... Read more ›
Efficient classical simulation of quantum Hamiltonian dynamics is often bottlenecked by exponential state growth and the overhead of generic sparse linear algebra. We introduce diagonal-budgeted Trotterization, a structure-aware strategy that decomposes Hamiltonians into factors preserving diagonal sparsity while tightly controlling fidelity loss. Our implementation, HamSim, utilizes a compact diagonal-sparse data layout and specialized C++/CU... Read more ›
The coordinated attack problem models the challenge of coordinating a joint action within a bounded time by communicating over unreliable links. It was the first distributed computing problem proven unsolvable. Its analysis also revealed the importance of common knowledge, a central concept in epistemic logic. However, the randomized version of coordinated attack, which is solvable, has not, to the best of our knowledge, been studied through the... Read more ›
Perfect resource placements in dense Eisenstein--Jacobi (EJ) networks partition the network into hexagonal radius-$t$ service cells. This paper studies local repair of such placements after resource failures. For one failed resource, we prove that one replacement cannot cover the failed hexagon and two always suffice, giving $\rho_{\mathrm{EJ}}(t)=2$ for all $t\ge1$. Among minimum-size repairs, the sharp minimum-overlap formula $\Omega_{\mathrm{... Read more ›
Debugging data races is a major challenge for students learning parallel programming due to the non-deterministic nature of concurrent execution and the complexity of shared-memory semantics. Recent advances in Large Language Models (LLMs) suggest that they could serve as AI teaching assistants, but the capabilities of lower-cost open-weight models for parallel debugging remain unclear. In this paper, we evaluate two Gemma4 open-weight models, G... Read more ›
Rahul M. Juliato has an informative post on what’s coming in Emacs 31. Juliato doesn’t mind living on the edge and has been tracking and using Emacs from the Master and emacs-31 branches. He says he likes to know “what’s in the box” and the way to learn what’s coming is to is to live in it. That’s a little too exciting for me and perhaps for you but Juliato’s post gives us a view of what to expect. Read more ›
Existing Decentralised Identifier (DID) methods require coordination, an agreed global order of operations, to update a DID document: blockchain-anchored methods incur fees and latency; lightweight peer methods (did:key, did:peer) offer no update mechanism; and Sidetree methods still require blockchain ordering for finality. We present did:crdt, a DID method that targets W3C DID Core and removes the need for coordination entirely: there is no le... Read more ›
Dense Gaussian networks are degree-four algebraic interconnection networks with compact diameter and simple modular routing. This paper studies non-redundant one-to-all broadcast repair in the dense Gaussian network generated by $\alpha=k+(k+1)i$. We propose multi-orientation edge-minimum repair (MOEM), which evaluates a constant-size family of Gaussian broadcast-tree orientations, selects a fault-aware orientation, contracts the fault-pruned tr... Read more ›
Diffusion models are now a dominant approach for high-fidelity image and video generation, yet scaling their training across GPU clusters remains challenging. Unlike transformer-only architectures, diffusion backbones commonly adopt UNet-style encoder-decoder structures with heterogeneous layers and long-range skip connections. Under conventional pipeline parallelism, these non-local dependencies force large skip activations and their gradients ... Read more ›
Fault-tolerant broadcasting in dense Eisenstein--Jacobi networks requires efficient recovery when faulty nodes disrupt the original broadcast structure. A re-rooting-based method guarantees that, for any two faulty nodes, a valid new source exists at maximum graph distance from both faults. However, identifying such a source without scanning the network or testing all boundary candidates remains an open practical problem. This paper presents a c... Read more ›
Dense Eisenstein--Jacobi (EJ) networks are degree-six algebraic interconnection networks whose finite quotient geometry is naturally represented by a hexagonal axial-coordinate ball. This paper studies non-redundant one-to-all broadcast repair in the dense EJ network generated by $\alpha=(t+1)+t\omega$, where $t$ is the network diameter. We propose EJ-MOEM, a multi-orientation edge-minimum repair method that evaluates a constant-size family of h... Read more ›
Perfect resource placement in dense Gaussian networks partitions the network into Lee balls centered at resource nodes. The fault-free placement problem is already classified; this paper studies the complementary post-deployment problem of repairing such placements after resource faults. The paper gives exact local repair theorems for the dense Gaussian placement generated by $t+(t+1)i$; by conjugation and rotation symmetry, the same results hol... Read more ›
Fault-tolerant broadcasting in dense Gaussian networks is recovered by re-rooting the broadcast at a new source at maximum graph distance from the faulty nodes. This paper extends the re-rooting framework by replacing its boundary-search source-selection step with a quotient-lattice-aware algebraic construction. The first contribution is a constant-time counting method for valid new sources, formulated as an intersection of two diameter-$k$ boun... Read more ›
Dense Gaussian networks provide degree-4 interconnection topologies with small diameter and regular structure, making them suitable for efficient one-to-all broadcasting. However, node failures can disrupt the broadcast process when faulty nodes occupy internal forwarding positions. This paper proposes a lightweight fault-tolerant broadcasting method based on dynamic source relocation, or re-rooting. Instead of constructing redundant spanning tr... Read more ›
Dense Eisenstein--Jacobi networks are degree-six algebraic interconnection topologies with regular structure, vertex symmetry, small diameter, and efficient communication algorithms. These properties make them suitable for parallel and on-chip communication systems in which collective operations such as one-to-all broadcasting are frequent. Existing optimal broadcasting algorithms for dense hexagonal/Eisenstein--Jacobi networks assume fault-free... Read more ›