The Betti poset in monomial resolutions

Let $P$ be a finite partially ordered set with unique minimal element $\hat{0}$. We study the Betti poset of $P$, created by deleting elements $q\in P$ for which the open interval $(\hat{0}, q)$ is acyclic. Using basic simplicial topology, we demonstrate an isomorphism in homology between open intervals of the form $(\hat{0},p)\subset P$ and corresponding open intervals in the Betti poset. Our motivating application is that the Betti poset of a monomial ideal's lcm-lattice encodes both its $\mathbb{Z}^{d}$-graded Betti numbers and the structure of its minimal free resolution. In the case of rigid monomial ideals, we use the data of the Betti poset to explicitly construct the minimal free resolution. Subsequently, we introduce the notion of rigid deformation, a generalization of Bayer, Peeva, and Sturmfels' generic deformation

The diurnal cycle of precipitation over the maritime continent in a high-resolution atmospheric model

Climate models can exhibit systematic errors in their mean precipitation over the Maritime Continent of the Indonesian archipelago at the heart of the tropical warm pool. These can often be traced back to an erroneous simulation of the diurnal cycle, and can lead to errors in global climate, through planetary wave propagation. Here, we examine the simulation of the diurnal cycle over the Maritime Continent in a series of high-resolution integrations of the UK Met Office atmospheric model, with horizontal resolutions of 40 and 12 km (where the convection is parametrised) and 4 km (where the convection is explicitly resolved), as part of the Cascade project. In these models, the vertical heating profile over the islands changes from a convective profile with a mid-tropospheric maximum in the early afternoon to a more stratiform profile with upper-tropospheric heating and mid-tropospheric cooling later. The convective heating profile forces a first internal mode gravity wave that propagates rapidly offshore; the deep warm anomalies behind its downwelling wavefront suppress convection offshore during early afternoon. The stratiform heating profile forces a gravity wave with a higher-order vertical mode that propagates slowly offshore later in the afternoon. This mode has a negative, destabilising temperature anomaly in the mid-troposphere. Together with the convergence zone between the wave fronts of the two modes, favourable conditions are created for offshore convection. In the 4 km explicit convection model, the offshore convection responds strongly to this gravity wave forcing, in agreement with observations, supporting a gravity wave–convection paradigm for the diurnal cycle over the Maritime Continent. However, the convective response in the lower-resolution models is much less coherent, leading to errors in the diurnal cycle and mean precipitation. Hence, to improve climate model simulations, sensitivity to gravity wave forcing should be a factor in future convective parametrisation schemes

Supplemental Aesthetics: Techniques in Live Performance

In this essay, I make a bid for the incorporation of the Derridian supplement into aesthetic discourses as a means of understanding and evaluating live performance. I call this move “supplemental aesthetics,” which, in the end, expands the vocabulary of absence and presence. I contend that a method of supplemental aesthetics adapts Derridian vocabulary to account for the intertextual and multisensory experience of live performance, asking practitioners and scholars to account for both the present and absent aspects of staged production. Supplemental aesthetics encourages a dialectic understanding of aesthetics: we make meaning by the simultaneous experience of reading what is present and what is absent on stage

The Ohio State University Endeavor Center

IMPACT. 1: Created more than 1,100 high-skill, high-wage jobs, adding more than $100 million of direct economic activity to the local community. -- 2. In cooperation with the Small Business Development Center of Ohio, sponsored or conducted 300 business workshops, training sessions, and seminars with nearly 5,000 attendees – business owners, prospective entrepreneurs, and ambitious employees seeking to improve the profitability of their businesses so they can grow and provide additional employment opportunities for those in the community. -- 3. Directly and intimately assisted over 100 small businesses tackle obstacles to growth, supplying strategic and space resources required for expansion, resulting in the graduation of more than two dozen partners to the construction of their own facilities or expansion into larger facilities in the local commercial real estate market.OSU PARTNERS: College of Food, Agricultural, and Environmental SciencesCOMMUNITY PARTNERS: U.S. Department of Commerce Economic Development Organization; United States Department of Agriculture; Governor's Office of Appalachia; Southern Ohio Diversification Initiative; Southern Ohio Agriculture and Community Development Foundation; Shawnee State University; Numerous small and large businessesPRIMARY CONTACT: Ryan Mapes ([email protected])Open since 2005, The Ohio State University Endeavor Center, a 27,000 square-foot mixed-use business incubator, has come to be recognized as a community leader in economic development, business training, and technological excellence. The original 26 permanent office spaces were expanded to 31 to satisfy demand for the flexible and professional office space provided in the facility for new and growing businesses. The latest renovation was completed to house the Manufacturing and Technology Small Business Development Specialist – a position designed to provide assistance for small manufacturers in Southern Ohio. The facility housed 24 individual businesses during the year and operated at 100% of its original occupancy capability. Endeavor Center business partners continually drive a surge in hiring, adding high-skill, high-wage positions throughout the year