Categorification of ice quiver mutation

In 2009, Keller and Yang categorified quiver mutation by interpreting it in terms of equivalences between derived categories. Their approach was based on Ginzburg's Calabi-Yau algebras and on Derksen-Weyman-Zelevinsky's mutation of quivers with potential. Recently, Matthew Pressland has generalized mutation of quivers with potential to that of ice quivers with potential. In this paper, we show that his rule yields derived equivalences between the associated relative Ginzburg algebras, which are special cases of Yeung's deformed relative Calabi-Yau completions arising in the theory of relative Calabi-Yau structures due to To\"en and Brav-Dyckerhoff. We illustrate our results on examples arising in the work of Baur-King-Marsh on dimer models and cluster categories of Grassmannians. We also give a categorification of mutation at frozen vertices as it appears in recent work of Fraser-Sherman-Bennett on positroid cluster structures.Comment: 34 pages; arXiv admin note: text overlap with arXiv:0906.0761, arXiv:1810.01179 by other authors; many improvements and corrections;to appear in Mathematische Zeitschrif

Brand Reputation and the Cost of Capital: Evidence of Adopting a Brand Name as the Corporate Name

This paper studies how the capital market perceives brand name adoption. I distinguish between brand adoption and radical type of corporate name change. A brand adoption name change occurs when the firm adopts one of its well-established brands as its new corporate name and a radical type occurs when the new name is semantically unrelated to firm history. Improved profitability and increased net investment accompany brand name adoption. After controlling for changes in the competing information sources, the accompanying improved economic performance, and the endogeneity of the decision to adopt a brand name, I find that, while there are no intertemporal variations in the cost of capital for a radical name change, a brand name adoption is associated with a lower cost of capital following the name change, suggesting that brand reputation is a valuable asset

Relative cluster categories and Higgs categories

Cluster categories were introduced in 2006 by Buan-Marsh-Reineke-Reiten-Todorov in order to categorify acyclic cluster algebras without coefficients. Their construction was generalized by Amiot (2009) and Plamondon (2011) to arbitrary cluster algebras associated with quivers. A higher dimensional generalization is due to Guo (2011). Cluster algebras with coefficients are important since they appear in nature as coordinate algebras of varieties like Grassmannians, double Bruhat cells, unipotent cells, etc. The work of Geiss-Leclerc-Schr\"oer often yields Frobenius exact categories which allow to categorify such cluster algebras. In this paper, we generalize the construction of (higher) cluster categories by Claire Amiot and by Lingyan Guo to the relative context. We prove the existence of an $n$-cluster tilting object in a Frobenius extriangulated category, namely the Higgs category (generalizing the Frobenius categories of Geiss-Leclerc-Schr\"oer), which is stably $n$-Calabi--Yau and Hom-finite, arising from a left $(n+1)$-Calabi--Yau morphism. Our results apply in particular to relative Ginzburg dg algebras coming from ice quivers with potential and higher Auslander algebras associated to $n$-representation-finite algebras.Comment: 72 page

AN INDOOR BLUETOOTH-CENTRIC PROXIMITY BASED POSITIONING SYSTEM

In recent years, positioning and navigation become an important topic in research. The most popular positioning system is an outdoor positioning called Global Positioning System (GPS). However, due to the influence of weak signal strength, weather conditions, diverse geographical and living environments, GPS sometimes cannot support indoor positioning and, if it can, the 5-10 meters error range does not meet the indoor positioning requirement. In order to provide a better solution with higher accuracy for indoor localization, we can benefit from the proliferation of indoor communication devices. Different technologies such as WiFi, Radio Frequency Identification (RFID) and Ultra-wideband (UWB) have been commonly used in indoor positioning systems. However, WiFi has a high energy consumption for indoor localization, as it consumes 3 to 10 watts per hour in the case of using 3 routers to do the job. In addition, due to its dependency on reference tags, the overall cost of the RFID-based approaches may usually cost more than $300 which is economically prohibitive. In terms of UWB, its low area coverage brings great challenges to popularizing its acceptance as a device for indoor positioning. The Bluetooth Low Energy (BLE) based iBeacon solution primarily focuses on the proximity based detection, and its low power consumption and low price bring great potential for its popularity. In this report, assuming that the resident owns a smartphone which is powered on, we present an iBeacon based indoor positioning system and provide some strategies and algorithms to overcome the indoor noise of possibly weak indoor Bluetooth signals. In our system, the Received Signal Strength Index (RSSI) is pre-processed to eliminate noise. Then, the distance between a mobile device and a BLE signal source can be calculated by combination use of pre-processed RSSI, Kalman Filter, and machine learning. In the end, the current mobile device position can be determined by using a triangulation algorithm. Our experimental results, acquired through running experiments in a real-world scenario, show that the localization error can be as low as 0.985m in the 2D environment. We also compared our results against other works with the same research objectives

Self-enhanced mobility enables vortex pattern formation in living matter

Emergence of regular spatial patterns is a hallmark in living matter ranging from subcellular organelles to developing embryos and to ecosystems. Mechanisms for the formation of ordered spatial patterns in biology often require chemical signaling that coordinates cellular behavior and differentiation. Here we discovered a novel route to large-scale regular pattern formation in living matter mediated by purely physical interactions. We found that dense bacterial living matter spontaneously developed an ordered lattice of mesoscale, fast-spinning vortices each consisting of ~10^4-10^5 motile cells; these mesoscale vortices were arranged in space over centimeter scale with apparent hexagonal order, while individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility of individual cells in the system. Our findings demonstrate a simple physical mechanism for self-organized pattern formation in living systems and more generally, in other active matter systems near the boundary of fluidlike and solidlike behaviors

Water Reservoir Maintained by Cell Growth Fuels the Spreading of a Bacterial Swarm

Flagellated bacteria can swim across moist surfaces within a thin layer of fluid, a means for surface colonization known as swarming. This fluid spreads with the swarm, but how it does so is unclear. We used micron-sized air bubbles to study the motion of this fluid within swarms of Escherichia coli. The bubbles moved diffusively, with drift. Bubbles starting at the swarm edge drifted inward for the first 5 s and then moved outward. Bubbles starting 30 μm from the swarm edge moved inward for the first 20 s, wandered around in place for the next 40 s, and then moved outward. Bubbles starting at 200 or 300 μm from the edge moved outward or wandered around in place, respectively. So the general trend was inward near the outer edge of the swarm and outward farther inside, with flows converging on a region about 100 μm from the swarm edge. We measured cellular metabolic activities with cells expressing a short-lived GFP and cell densities with cells labeled with a membrane fluorescent dye. The fluorescence plots were similar, with peaks about 80 μm from the swarm edge and slopes that mimicked the particle drift rates. These plots suggest that net fluid flow is driven by cell growth. Fluid depth is largest in the multilayered region between approximately 30 and 200 μm from the swarm edge, where fluid agitation is more vigorous. This water reservoir travels with the swarm, fueling its spreading. Intercellular communication is not required; cells need only grow.Molecular and Cellular BiologyPhysic

Relative cluster categories and Higgs categories with infinite-dimensional morphism spaces

Cluster algebras *with coefficients* are important since they appear in nature as coordinate algebras of varieties like Grassmannians, double Bruhat cells, unipotent cells, ... . The approach of Geiss-Leclerc-Schr\"oer often yields Frobenius exact categories which allow to categorify such cluster algebras. In previous work, the third-named author has constructed Higgs categories and relative cluster categories in the relative Jacobi-finite setting (arXiv:2109.03707). Higgs categories generalize the Frobenius categories used by Geiss-Leclerc-Schr\"oer. In this article, we construct the Higgs category and the relative cluster category in the relative Jacobi-infinite setting under suitable hypotheses. This covers for example the case of Jensen-King-Su's Grassmannian cluster category. As in the relative Jacobi-finite case, the Higgs category is no longer exact but still extriangulated in the sense of Nakaoka-Palu. We also construct a cluster character refining Plamondon's. In the appendix, Chris Fraser and the second-named author categorify quasi-cluster morphisms using Frobenius categories. A recent application of this result is due to Matthew Pressland, who uses it to prove a conjecture by Muller-Speyer.Comment: 44 pages, with an appendix by Chris Fraser and Bernhard Keller; v2: Corrections in abstract, references and addres