Variations on Cops and Robbers

We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R > 1 edges at a time, establishing a general upper bound of N / \alpha ^{(1-o(1))\sqrt{log_\alpha N}}, where \alpha = 1 + 1/R, thus generalizing the best known upper bound for the classical case R = 1 due to Lu and Peng. We also show that in this case, the cop number of an N-vertex graph can be as large as N^{1 - 1/(R-2)} for finite R, but linear in N if R is infinite. For R = 1, we study the directed graph version of the problem, and show that the cop number of any strongly connected digraph on N vertices is at most O(N(log log N)^2/log N). Our approach is based on expansion.Comment: 18 page

Packing tight Hamilton cycles in 3-uniform hypergraphs

Let H be a 3-uniform hypergraph with N vertices. A tight Hamilton cycle C \subset H is a collection of N edges for which there is an ordering of the vertices v_1, ..., v_N such that every triple of consecutive vertices {v_i, v_{i+1}, v_{i+2}} is an edge of C (indices are considered modulo N). We develop new techniques which enable us to prove that under certain natural pseudo-random conditions, almost all edges of H can be covered by edge-disjoint tight Hamilton cycles, for N divisible by 4. Consequently, we derive the corollary that random 3-uniform hypergraphs can be almost completely packed with tight Hamilton cycles w.h.p., for N divisible by 4 and P not too small. Along the way, we develop a similar result for packing Hamilton cycles in pseudo-random digraphs with even numbers of vertices.Comment: 31 pages, 1 figur

Few-Shot Image Recognition by Predicting Parameters from Activations

In this paper, we are interested in the few-shot learning problem. In particular, we focus on a challenging scenario where the number of categories is large and the number of examples per novel category is very limited, e.g. 1, 2, or 3. Motivated by the close relationship between the parameters and the activations in a neural network associated with the same category, we propose a novel method that can adapt a pre-trained neural network to novel categories by directly predicting the parameters from the activations. Zero training is required in adaptation to novel categories, and fast inference is realized by a single forward pass. We evaluate our method by doing few-shot image recognition on the ImageNet dataset, which achieves the state-of-the-art classification accuracy on novel categories by a significant margin while keeping comparable performance on the large-scale categories. We also test our method on the MiniImageNet dataset and it strongly outperforms the previous state-of-the-art methods

Extrusion-based Direct Write of Functional Materials From Electronics to Magnetics

New micro- and nanoscale fabrication methods are of vital importance to drive scientific and technological advances in electronics, materials science, physics and biology areas. Direct ink writing (DW) describes a group of mask-less and contactless additive manufacturing (AM), or 3D printing, processes that involve dispensing inks, typically particle suspensions, through a deposition nozzle to create 2D or 3D material patterns with desired architecture and composition on a computer-controlled movable stage. Much of the functional material printing and electronics area remains underdeveloped for this new technology. There is a need to understand and establish the advantages and shortcomings of extrusion-based DW over other AM technologies for various applications. Further, the integration of extrusion DW with other AM technologies, such as stereolithography (SLA), remains an active area of research. In this study, we performed a comprehensive study of the relationships between ink properties/machine parameters and the printed line dimensions, including parametric studies of the machine parameters, an in-nozzle flow dynamics simulation, and a preliminary 3D comprehensive flow dynamics simulation. We explored the boundary and possibilities of extrusion-based DW. We pushed the limit of DW printing resolution, solid content of nonspherical particles, and printed polymer-bonded magnets with the highest density and magnetic performance among all 3D printing magnet techniques. We optimized the design of DW ink from rheological, mechanical, and microscopic perspectives. We are one of the first experimentalists as of author’s knowledge to perform bimodal highly concentrated suspension rheology analysis using nonspherical particles. Great improvements in solid loading were achieved by using the best large-to-small particle size ratio and large particle volume ratio found. The data and analysis could provide a new standard and solid experimental support for functional material printing

Ramsey games with giants

The classical result in the theory of random graphs, proved by Erdos and Renyi in 1960, concerns the threshold for the appearance of the giant component in the random graph process. We consider a variant of this problem, with a Ramsey flavor. Now, each random edge that arrives in the sequence of rounds must be colored with one of R colors. The goal can be either to create a giant component in every color class, or alternatively, to avoid it in every color. One can analyze the offline or online setting for this problem. In this paper, we consider all these variants and provide nontrivial upper and lower bounds; in certain cases (like online avoidance) the obtained bounds are asymptotically tight.Comment: 29 pages; minor revision

Multi-stage Multi-recursive-input Fully Convolutional Networks for Neuronal Boundary Detection

In the field of connectomics, neuroscientists seek to identify cortical connectivity comprehensively. Neuronal boundary detection from the Electron Microscopy (EM) images is often done to assist the automatic reconstruction of neuronal circuit. But the segmentation of EM images is a challenging problem, as it requires the detector to be able to detect both filament-like thin and blob-like thick membrane, while suppressing the ambiguous intracellular structure. In this paper, we propose multi-stage multi-recursive-input fully convolutional networks to address this problem. The multiple recursive inputs for one stage, i.e., the multiple side outputs with different receptive field sizes learned from the lower stage, provide multi-scale contextual boundary information for the consecutive learning. This design is biologically-plausible, as it likes a human visual system to compare different possible segmentation solutions to address the ambiguous boundary issue. Our multi-stage networks are trained end-to-end. It achieves promising results on two public available EM segmentation datasets, the mouse piriform cortex dataset and the ISBI 2012 EM dataset.Comment: Accepted by ICCV201