Traditional layered graph depictions such as flow charts are in wide use. Yet as graphs grow more complex, these depictions can become difficult to understand. Quilts are matrix-based depictions for layered graphs designed to address this problem. In this research, we first improve Quilts by developing three design alternatives, and then compare the best of these alternatives to better-known node-link and matrix depictions. A primary weakness in Quilts is their depiction of skip links, links that do not simply connect to a succeeding layer. Therefore in our first study, we compare Quilts using color-only, text-only, and mixed (color and text) skip link depictions, finding that path finding with the color-only depiction is significantly slower and less accurate, and that in certain cases, the mixed depiction offers an advantage over the text-only depiction. In our second study, we compare Quilts using the mixed depiction to node-link diagrams and centered matrices. Overall results show that users can find paths through graphs significantly faster with Quilts (46.6 secs) than with node-link (58.3 secs) or matrix (71.2 secs) diagrams. This speed advantage is still greater in large gra
In this paper, we present new objects, quilts of alternating sign matrices with respect to two given posets. Quilts generalize several commonly used concepts in mathematics. For example, the rank function on submatrices of a matrix gives rise to a quilt with respect to two Boolean lattices. When the two posets are chains, a quilt is equivalent to an alternating sign matrix and its corresponding corner sum matrix. Quilts also generalize the monotone Boolean functions counted by the Dedekind numbers. Quilts form a distributive lattice with many beautiful properties and contain many classical and well-known sublattices, such as the lattice of matroids of a given rank and ground set. While enumerating quilts is hard in general, we prove two major enumerative results, when one of the posets is an antichain and when one of them is a chain. We also give some bounds for the number of quilts when one poset is the Boolean lattice.
In the author's previous paper, the author constructed holomorphic quilts from the bigons of the Lagrangian Floer chain group after performing Lagrangian composition. This paper proves the uniqueness of such holomorphic quilts. As a consequence, it provides a combinatorial method for computing the boundary map of immersed Lagrangian Floer chain groups when the symplectic manifolds are closed surfaces. One outcome is the construction of many examples exhibiting figure eight bubbling, which also confirms a conjecture of Cazassus Herald Kirk Kotelskiy.
We study the entanglement dynamics of a family of quantum collision models by analytically solving the pairwise concurrence for all qubit pairs. We introduce a diagrammatic method that offers an intuitive, frame-by-frame understanding of these dynamics. This allows us to monitor how a single collision affects the entanglement of the whole many-body system in some special cases. We focus on a class of models where the square of concurrence is a conserved quantity in the qubit collisions, aiding us to formulate general rules of entanglement propagation. In particular, among the multiple examples we will be showing, we identify a type of genuine multipartite entanglement, which we refer to as \textit{entanglement quilt}, where every qubit is entangled with every other qubit. We find that in some models, an entanglement quilt is hypersensitive to local excitation fluctuations: The presence of even a single excited qubit can destroy the entanglement quilts. We offer a detailed mathematical treatment on the phenomena, which can help us understand the disappearance of long-range entanglement in condensed matter systems above zero temperature. We also speculate about a possible property of
In this article, we modify the proof of holomorphic quilts from Wehrheim and Woodward in \cite{wehrheim2009floer} to construct a specific type of immersed holomorphic quilt, where the symplectic manifolds are closed surfaces. The application is to compare Lagrangian Floer theory with quilted Lagrangian Floer theory, as they relate through Lagrangian correspondence. A potential example is provided to support Bottman and Wehrheim's conjecture \cite{bottman2018gromov} regarding the isomorphism between Lagrangian Floer homology and quilted Lagrangian Floer homology after twisting by bounding cochains.
Self-heating is a severe problem for high-power GaN electronic and optoelectronic devices. Various thermal management solutions, e.g. flip-chip bonding or composite substrates have been attempted. However, temperature rise still limits applications of the nitride-based technology. Here we demonstrate that thermal management of GaN transistors can be substantially improved via introduction of the alternative heat-escaping channels implemented with few-layer graphene - an excellent heat conductor. We have transferred few-layer graphene to AlGaN/GaN heterostructure field-effect transistors on SiC substrates to form the "graphene-graphite quilts" - lateral heat spreaders, which remove heat from the channel regions. Using the micro-Raman spectroscopy for in-situ monitoring we have shown that temperature can be lowered by as much as ~ 20oC in such devices operating at ~13-W/mm power density. The simulations suggest that the efficiency of the "graphene quilts" can be made even higher in GaN devices on thermally resistive sapphire substrates and in the designs with the closely located heat sinks. Our results open a novel application niche for few-layer graphene in high-power electronics.
Lighten your pack this summer—skip the sleeping bag and carry one of our favorite ultralight backpacking quilts instead
A `transplantable pair' is a pair of glueing diagrams that can be used to create pairs of plane domains that are isospectral for the Laplace operator. We present a host of transplantable pairs worked out by John Conway using his theory of quilts
Associated to a symplectic quotient $M/\!/G$ is a Lagrangian correspondence $Λ_G$ from $M/\!/G$ to $M$. In this note, we construct in two examples quilts with seam condition on such a correspondence, in the case of $S^1$ acting on $\mathbb{CP}^2$ with symplectic quotient $\mathbb{CP}^2/\!/ S^1 = \mathbb{CP}^1$. First, we study the quilted strips that would, if not for figure eight bubbling, identify the Floer chain groups $CF(γ,S_{\text{Cl}}^1)$ and $CF(\mathbb{RP}^2,T_{\text{Cl}}^2)$, where $γ$ is the connected double-cover of $\mathbb{RP}^1$. Second, we answer a question due to Akveld-Cannas da Silva-Wehrheim by explicitly producing a figure eight bubble which obstructs an isomorphism between two Floer chain groups. The figure eight bubbles we construct in this paper are the first concrete examples of this phenomenon.
We construct orientations on moduli spaces of pseudoholomorphic quilts with seam conditions in Lagrangian correspondences equipped with relative spin structures and determine the effect of various gluing operations on the orientations. We also investigate the behavior of the orientations under composition of Lagrangian correspondences.
We show that the novel figure eight singularity in a pseudoholomorphic quilt can be continuously removed when composition of Lagrangian correspondences is cleanly immersed. The proof of this result requires a collection of width-independent elliptic estimates that allow for non-standard complex structures on the domain.
We further study the symplectic Khovanov homology of Seidel and Smith and its generalization to even tangles. This homology theory is a conjectural geometric model for Khovanov homology. In this paper we uncover structures on symplectic Khovanov homology which have analogues in Khovanov homology. To each elementary (as well as minimal) cobordism between two tangles we associate a homomorphism between the symplectic Khovanov homology groups of the two tangles. We define the symplectic analogues $H_{s}^m$ of Khovanov's arc algebras and equip the symplectic Khovanov homology of an $(m,n)$-tangle with the structure of an $(H_{s}^m,H_{s}^n)$-bimodule. We show that $H_{s}^m$ and Khovanov's $H^m$ are isomorphic as associative algebras over $\Z/2$. We also obtain a skein exact triangle for symplectic Khovanov homology which resembles the one for Khovanov homology.
We define relative Floer theoretic invariants arising from 'quilted pseudo-holomorphic surfaces': Collections of pseudoholomorphic maps to various target spaces with 'seam conditions' in Lagrangian correspondences. As application we construct a morphism on quantum homology associated to any monotone Lagrangian correspondence.
We establish a Gromov compactness theorem for strip shrinking in pseudoholomorphic quilts when composition of Lagrangian correspondences is immersed. In particular, we show that figure eight bubbling occurs in the limit, argue that this is a codimension-$0$ effect, and predict its algebraic consequences -- geometric composition extends to a curved $A_\infty$-bifunctor, in particular the associated Floer complexes are isomorphic after a figure eight correction of the bounding cochain. An appendix with Felix Schmäschke provides examples of nontrivial figure eight bubbles.
We investigated the impact of incorporating quantitative reasoning for deeper sense-making in a Quantum Interactive Learning Tutorial (QuILT) on students' conceptual performance using a framework emphasizing integration of conceptual and quantitative aspects of quantum optics. In this investigation, we compared two versions of the QuILT that were developed and validated to help students learn various aspects of quantum optics using a Mach Zehnder Interferometer with single photons and polarizers. One version of the QuILT is entirely conceptual while the other version integrates quantitative and conceptual reasoning (hybrid version). Performance on conceptual questions of upper-level undergraduate and graduate students who engaged with the hybrid QuILT was compared with that of those who utilized the conceptual QuILT emphasizing the same concepts. Both versions of the QuILT focus on the same concepts, use a scaffolded approach to learning, and take advantage of research on students' difficulties in learning. The hybrid and conceptual QuILTs were used in courses for upper-level undergraduates or first-year physics graduate students in several consecutive years at the same university.
In this work, we propose a novel strategy to ensure infants, who inadvertently displace their quilts during sleep, are promptly and accurately re-covered. Our approach is formulated into two subsequent steps: interference resolution and quilt spreading. By leveraging the DWPose human skeletal detection and the Segment Anything instance segmentation models, the proposed method can accurately recognize the states of the infant and the quilt over her, which involves addressing the interferences resulted from an infant's limbs laid on part of the quilt. Building upon prior research, the EM*D deep learning model is employed to forecast quilt state transitions before and after quilt spreading actions. To improve the sensitivity of the network in distinguishing state variation of the handled quilt, we introduce an enhanced loss function that translates the voxelized quilt state into a more representative one. Both simulation and real-world experiments validate the efficacy of our method, in spreading and recover a quilt over an infant.
The QUILT-1M dataset is the first openly available dataset containing images harvested from various online sources. While it provides a huge data variety, the image quality and composition is highly heterogeneous, impacting its utility for text-conditional image synthesis. We propose an automatic pipeline that provides predictions of the most common impurities within the images, e.g., visibility of narrators, desktop environment and pathology software, or text within the image. Additionally, we propose to use semantic alignment filtering of the image-text pairs. Our findings demonstrate that by rigorously filtering the dataset, there is a substantial enhancement of image fidelity in text-to-image tasks.
We prove an analog of the Deligne conjecture for prestacks. We show that given a prestack $\mathbb A$, its Gerstenhaber--Schack complex $\mathbf{C}_{\mathsf{GS}}(\mathbb A)$ is naturally an $E_2$-algebra. This structure generalises both the known $\mathsf{L}_\infty$-algebra structure on $\mathbf{C}_{\mathsf{GS}}(\mathbb A)$, as well as the Gerstenhaber algebra structure on its cohomology $\mathbf{H}_{\mathsf{GS}}(\mathbb A)$. The main ingredient is the proof of a conjecture of Hawkins \cite{hawkins}, stating that the dg operad $\mathsf{Quilt}$ has vanishing homology in positive degrees. As a corollary, $\mathsf{Quilt}$ is quasi-isomorphic to the operad $\mathsf{Brace}$ encoding brace algebras. In addition, we improve the $L_\infty$-structure on $\mathsf{Quilt}$ by showing that it originates from a $\mathsf{PreLie}_\infty$-structure lifting the $\mathsf{PreLie}$-structure on $\mathsf{Brace}$ in homology.
Continuous machine learning pipelines are common in industrial settings where models are periodically trained on data streams. Unfortunately, concept drifts may occur in data streams where the joint distribution of the data X and label y, P(X, y), changes over time and possibly degrade model accuracy. Existing concept drift adaptation approaches mostly focus on updating the model to the new data possibly using ensemble techniques of previous models and tend to discard the drifted historical data. However, we contend that explicitly utilizing the drifted data together leads to much better model accuracy and propose Quilt, a data-centric framework for identifying and selecting data segments that maximize model accuracy. To address the potential downside of efficiency, Quilt extends existing data subset selection techniques, which can be used to reduce the training data without compromising model accuracy. These techniques cannot be used as is because they only assume virtual drifts where the posterior probabilities P(y|X) are assumed not to change. In contrast, a key challenge in our setup is to also discard undesirable data segments with concept drifts. Quilt thus discards drifted d
Diagnosis in histopathology requires a global whole slide images (WSIs) analysis, requiring pathologists to compound evidence from different WSI patches. The gigapixel scale of WSIs poses a challenge for histopathology multi-modal models. Training multi-model models for histopathology requires instruction tuning datasets, which currently contain information for individual image patches, without a spatial grounding of the concepts within each patch and without a wider view of the WSI. Therefore, they lack sufficient diagnostic capacity for histopathology. To bridge this gap, we introduce Quilt-Instruct, a large-scale dataset of 107,131 histopathology-specific instruction question/answer pairs, grounded within diagnostically relevant image patches that make up the WSI. Our dataset is collected by leveraging educational histopathology videos from YouTube, which provides spatial localization of narrations by automatically extracting the narrators' cursor positions. Quilt-Instruct supports contextual reasoning by extracting diagnosis and supporting facts from the entire WSI. Using Quilt-Instruct, we train Quilt-LLaVA, which can reason beyond the given single image patch, enabling diagno