Refined Asymptotics of the Finite-Size Magnetization via a New Conditional Limit Theorem for the Spin

We study the fluctuations of the spin per site around the thermodynamic magnetization in the mean-field Blume-Capel model. Our main theorem generalizes the main result in a previous paper (Ellis, Machta, and Otto) in which the first rigorous confirmation of the statistical mechanical theory of finite-size scaling for a mean-field model is given. In that paper our goal is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume-Capel model. The main result is that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter $\alpha$ governing the speed at which the sequence approaches criticality is below a certain threshold $\alpha_0$. Our main theorem in the present paper on the fluctuations of the spin per site around the thermodynamic magnetization is based on a new conditional limit theorem for the spin, which is closely related to a new conditional central limit theorem for the spin.Comment: 78 pages, 2 figure

Decision models for fast-fashion supply and stocking problems in internet fulfillment warehouses

Internet technology is being widely used to transform all aspects of the modern supply chain. Specifically, accelerated product flows and wide spread information sharing across the supply chain have generated new sets of decision problems. This research addresses two such problems. The first focuses on fast fashion supply chains in which inventory and price are managed in real time to maximize retail cycle revenue. The second is concerned with explosive storage policies in Internet Fulfillment Warehouses (IFW). Fashion products are characterized by short product life cycles and market success uncertainty. An unsuccessful product will often require multiple price discounts to clear the inventory. The first topic proposes a switching solution for fast-fashion retailers who have preordered an initial or block inventory, and plan to use channel switching as opposed to multiple discounting steps. The FFS Multi-Channel Switching (MCS) problem then is to monitor real-time demand and store inventory, such that at the optimal period the remaining store inventory is sold at clearance, and the warehouse inventory is switched to the outlet channel. The objective is to maximize the total revenue. With a linear projection of the moving average demand trend, an estimation of the remaining cycle revenue at any time in the cycle is shown to be a concave function of the switching time. Using a set of conditions the objective is further simplified into cases. The Linear Moving Average Trend (LMAT) heuristic then prescribes whether a channel switch should be made in the next period. The LMAT is compared with the optimal policy and the No-Switch and Beta-Switch rules. The LMAT performs very well and the majority of test problems provide a solution within 0.4% of the optimal. This confirms that LMAT can readily and effectively be applied to real time decision making in a FFS. An IFW is a facility built and operated exclusively for online retail, and a key differentiator is the explosive storage policy. Breaking the single stocking location tradition, in an IFW small batches of the same stock keeping unit (SKU) are dispersed across the warehouse. Order fulfillment time performance is then closely related to the storage location decision, that is, for every incoming bulk, what is the specific storage location for each batch. Faster fulfillment is possible when SKUs are clustered such that narrow band picklists can be efficiently generated. Stock location decisions are therefore a function of the demand arrival behavior and correlations with other SKUs. Faster fulfillment is possible when SKUs are clustered such that narrow band picklists can be efficiently generated. Stock location decisions are therefore a function of the demand behavior and correlations with other SKUs. A Joint Item Correlation and Density Oriented (JICDO) Stocking Algorithm is developed and tested. JICDO is formulated to increase the probability that M pick able order items are stocked in a δ band of storage locations. It scans the current inventory dispersion to identify location bands with low SKU density and combines the storage affinity with correlated items. In small problem testing against a MIP formulation and large scale testing in a simulator the JICDO performance is confirmed

Doctor of Philosophy

dissertationThe unstable expansion of the polyglutamine (polyQ) tract is a critical factor in the pathogenic pathway of at least ten neurodegenerative diseases, including Huntington's disease, spinal and bulbar muscular atrophy (SBMA), dentatorubral-pallidoluysian atrophy (DRPLA), and seven spinocerebellar ataxias, all of which are termed as polyglutamine diseases. One less understood but common feature of polyQ diseases is polyQ protein aggregation. This dissertation explores the protein folding, hydrogen bonding, and water accessibility changes which are induced by the enlargement of the polyQ tract using advanced informatics and computational methods, including protein 3D structure modeling and molecular dynamics simulations. This dissertation also demonstrates that these state-of-the-art computational and informatics methods are powerful tools to provide useful insights into protein aggregation in polyQ diseases. The enlargement of polyQ segments affects both local and global structures of polyQ proteins as well as their water-accessibility, hydrogen bond patterns, and other structural characteristics. Results from both isolated polyQ and polyQ segments in the context of ataxin-2 and ataxin-3 show that the polyQ tracts increasingly prefer self-interaction as the lengths of the tracts increase, indicating an increased tendency toward aggregation among larger polyQ tracts. These results provide new insights into possible pathogenic mechanisms of polyQ diseases based solely on the increased propensity toward polyQ aggregation and suggest that the modulation of solvent-polyQ interaction may be a possible therapeutic strategy for treating polyQ diseases. The analysis pipeline designed and used in this study is an effective way to study the molecular mechanism of polyQ diseases, and can be generalized to study other diseases associated with the protein conformation changes, such as Parkinson's disease, Alzheimer's disease, and cancer

Media as Other Information for Fundamental Valuation

The media is an important information intermediary. We investigate the informational role of the media by examining whether media content, measured by the sentiment of news articles, contains information about a firm’s fundamental value beyond that conveyed in earnings, book value, and analyst forecasts. We show that incorporating media content into Ohlson’s (1995) residual income model generally improves its ability to predict future residual income, explain current stock prices, and predict future stock prices. Our results are strengthened when media coverage is higher and when media sentiment is more disperse

Using Omnichannel Sales Data Analytics to Decide Between Store and Distribution Center Fulfillment Options

A brick-and-mortar retailer can fulfill online customer orders in two ways (i) Buy Online Fulfill from Store (BOFS) - Picked from store inventory, and (ii) Fulfill from Distribution Center (FDC) - Picked from DC or warehouse inventory. The fulfillment decision is made in real time for each order, with the primary goal of maximizing the revenue value of the store inventory. Analysis of sales data in both online and store channels is used to forecast the value of the dispersed inventory, and then develop a prescriptive model for making a fulfillment decision