Orbit spaces of free involutions on the product of two projective spaces

Let $X$ be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on $X$ and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the Leray spectral sequence associated to the Borel fibration $X \hookrightarrow X_{\mathbb{Z}_2} \longrightarrow B_{\mathbb{Z}_2}$. We also give an application of our result to show that if $X$ has the mod 2 cohomology algebra of the product of two real projective spaces (respectively complex projective spaces), then there does not exist any $\mathbb{Z}_2$-equivariant map from $\mathbb{S}^k \to X$ for $k \geq 2$ (respectively $k \geq 3$), where $\mathbb{S}^k$ is equipped with the antipodal involution.Comment: 14 pages, to appear in Results in Mathematic

Unsponsored ADRs Falling Through the Cracks: Adapting a Domestic Securities Regime to a Global Marketplace

Investing in the securities market has become a commonplace activity for expert and amateur investors alike. As more and more companies transcend national boundaries with their business activities, investment in their securities becomes coveted by international investors. Since securities are regulated on a country-by-country basis, it is unclear which law applies when conflict arises. In an attempt to clarify one such situation, simplify the application of US securities laws, and respect the legal regimes of other nations, the Morrison decision created an unclear test which leaves investors in unsponsored American Depositary Receipts (ADRs), one of the most common international trading mechanisms, completely unprotected by the laws of any securities regulatory regime. This Note proposes using existing infrastructure to facilitate the trade of unsponsored ADRs as a way to ensure both protection of investors and efficiency of the global securities market

Essays on Service Innovation

As economies are increasingly driven by services, the introduction of new services to satisfy customers and improve firm value is becoming a critical issue for managers. In my dissertation, I take a step in improving the understanding of service innovations. In the first essay, I look at the determinants of the number of service innovations introduced by a firm and their interrelationship with customer satisfaction and firm value. Furthermore, I look how these interrelationships vary between Internet-Enabled Service Innovations (IESIs) and Non-Internet-Enabled Service Innovations (NIESIs). I develop a system of equations that link service innovation, customer satisfaction and firm value. I model the determinants of service innovations, using a zero-inflated Poisson model. I estimate the model on a panel data set that I assembled across multiple industries from multiple data sources such as the American Customer Satisfaction Index, Compustat, SDC Platinum, and LexisNexis. My results reveal that IESIs are more strongly influenced by financial resources of the firm and by market growth than are NIESIs. Surprisingly, neither IESIs nor NIESIs have a significant direct effect on customer satisfaction. However, IESIs have a positive and significant effect on firm value. Given the differences between consumer markets and business markets, it is important to understand better the determinants and outcomes of business-to-business service innovations (B2B-SIs). In my second essay, I empirically address this issue. I develop a modeling system that relates service innovation to firm value. I estimate my model on unique panel data of service innovations. Results indicate that B2B-SIs have positive effects on firm value. Furthermore, I find that the number of B2B-SIs introduced by a firm is primarily determined by firm-level factors rather than marketlevel factors Overall, I find that regardless of firm type or market type, the number of service innovations introduced by a firm has a substantial impact on firm value. In particular, IESIs and B2B-SIs increase firm value. In addition, the two essays also show that liquid financial resources are important determinants of service innovations. This is especially true for IESIs and B2B-SIs

Radial Networks: Dynamic Layer Routing for High-Performance Large Language Models

Large language models (LLMs) often struggle with strict memory, latency, and power demands. To meet these demands, various forms of dynamic sparsity have been proposed that reduce compute on an input-by-input basis. These methods improve over static methods by exploiting the variance across individual inputs, which has steadily grown with the exponential increase in training data. Yet, the increasing depth within modern models, currently with hundreds of layers, has opened opportunities for dynamic layer sparsity, which skips the computation for entire layers. In this work, we explore the practicality of layer sparsity by profiling residual connections and establish the relationship between model depth and layer sparsity. For example, the residual blocks in the OPT-66B model have a median contribution of 5% to its output. We then take advantage of this dynamic sparsity and propose Radial Networks, which perform token-level routing between layers guided by a trained router module. These networks can be used in a post-training distillation from sequential networks or trained from scratch to co-learn the router and layer weights. They enable scaling to larger model sizes by decoupling the number of layers from the dynamic depth of the network, and their design allows for layer reuse. By varying the compute token by token, they reduce the overall resources needed for generating entire sequences. Overall, this leads to larger capacity networks with significantly lower compute and serving costs for large language models.Comment: First two authors have equal contributio

Exploring interannual variability in potential spawning habitat for Atlantic bluefin tuna in the Slope Sea

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Rypina, I. I., Dotzel, M. M., Pratt, L. J., Hernandez, C. M., & Llopiz, J. K. Exploring interannual variability in potential spawning habitat for Atlantic bluefin tuna in the Slope Sea. Progress in Oceanography, 192, (2021): 102514, https://doi.org/10.1016/j.pocean.2021.102514.The Slope Sea in the Northwest Atlantic Ocean, located between the Gulf Stream and the continental shelf of the Northeast United States, is a recently-documented possible major spawning ground for Atlantic bluefin tuna (Thunnus thynnus). Larval surveys and a habitat modeling study have shown that suitable spawning habitat occurs in the Slope Sea, but the degree to which this habitat varies interannually is an open question. Here, we perform a decade-long (2009–2018) numerical modeling analysis, with simulated larvae released uniformly throughout the Slope Sea, to investigate the interannual variability in the water temperature and circulation criteria deemed necessary for successful spawning. We also quantify the influence of Gulf Stream meanders and overshoot events on larval retention and their effect on habitat suitability rates throughout the Slope Sea, defined as the percentage of simulated larvae released at a given location that satisfy criteria related to water temperature and retention near nursery habitat. Average environmental oceanographic conditions over the decade are most favorable in the western part of the Slope Sea, specifically in the Slope Gyre and away from the immediate vicinity of the Gulf Stream. Variability in domain- and summertime-averaged yearly spawning habitat suitability rates is up to 25% of the mean decadal-averaged values. Yearly habitat suitability correlates strongly with the Gulf Stream overshoot but does not correlate well with other oceanographic variables or indices, so an overshoot index can be used as a sole oceanographic proxy for predicting yearly bluefin spawning habitat suitability in the Slope Sea. Selective spawning can weaken the correlation between habitat suitability and Gulf Stream overshoot. Effort should be put towards collecting observational data against which we could validate our findings.This work was funded by a US National Science Foundation (NSF) grant (OCE-1558806) awarded to IIR, LJP, and JKL. MMD was supported by an NSF Graduate Research Fellowship. CMH was partially supported by the Adelaide and Charles Link Foundation and the J. Seward Johnson Endowment in support of the Woods Hole Oceanographic Institution’s Marine Policy Center

Hierarchical ZSM‐5 catalysts: The effect of different intracrystalline pore dimensions on catalyst deactivation behaviour in the MTO reaction

We present the effect of different combinations of intracrystalline pore systems in hierarchical ZSM‐5 zeolites on their performance as MTO catalysts. We prepared ZSM‐5 zeolites with additional intracrystalline mesoporous, intracrystalline macropores and a novel ZSM‐5 type zeolite with intracrystalline meso and macropores. The catalytic results showed that both used catalysts with mesopores and macropores exhibited three times longer catalyst lifetime compared to a conventional catalyst. However, TGA analysis of the deactivated catalysts showed much larger coke content in the mesoporous catalyst than in the macroporous catalyst. Consequently, macropores predominantly led to reduced coke formation rate while additional mesopores predominantly enhanced the resistance against deactivation by coke. Combining both intracrystalline meso and macropores in one catalyst lead to a tenfold increase in catalyst lifetime. Besides the effect on the catalyst lifetime there was also a strong effect of the additional pore systems on the selectivity of the catalysts. The catalysts containing mesopores showed reduced selectivity to short chain olefins and increased selectivity to larger hydrocarbons in comparison to the catalysts without a mesopores system

Learning from Students: Applying t-Distributions to Explore Accurate and Efficient Formats for LLMs

The increasing size of large language models (LLMs) traditionally requires low-precision integer formats to meet strict latency and power demands. Yet recently, alternative formats such as Normal Float (NF4) have increased model accuracy at the cost of increased chip area. In this work, we first conduct a large-scale analysis of LLM weights and activations across 30 networks and conclude that most distributions follow a Student's t-distribution. We then derive a new theoretically optimal format, Student Float (SF4), that improves over NF4 across modern LLMs, for example increasing the average accuracy on LLaMA2-7B by 0.76% across tasks. Using this format as a high-accuracy reference, we then propose augmenting E2M1 with two variants of supernormal support for higher model accuracy. Finally, we explore the quality and efficiency frontier across 11 datatypes by evaluating their model accuracy and hardware complexity. We discover a Pareto curve composed of INT4, E2M1, and E2M1 with supernormal support, which offers a continuous tradeoff between model accuracy and chip area. For example, E2M1 with supernormal support increases the accuracy of Phi-2 by up to 2.19% with 1.22% area overhead, enabling more LLM-based applications to be run at four bits. The supporting code is hosted at https://github.com/cornell-zhang/llm-datatypes.Comment: Accepted to ICML 202

Success factors for service innovation: a meta-analysis

Service sectors form a considerable part of the world economy. Contrary to the logical assumption that service innovation research should represent a significant share of all innovation research, the vast majority of innovation studies focus on products as opposed to services. This research presents a meta-analysis of the antecedents of service innovation performance conducted on 92 independent samples obtained from 114 articles published between 1989 and 2015. This research contributes to our understanding of service innovation in three major ways. First, this is the first meta-analysis that specifically assesses the relative importance of antecedents of service innovation performance, while also pinpointing the differences in meta-analytic findings between antecedents of service and product innovation performance. Whilst there are some universal success factors that transcend the boundaries between services and products, the presence of marked differences implies that it would be wrong to treat the development of new services and new products as the same. Second, the meta-analysis demonstrates that the antecedents of service innovation performance are contingent on the sector context (i.e., explicit versus tacit services). Comparing results between products and services, and between tacit and explicit services, there appears to be a continuum where explicit services sit interstitial between tacit services on one side and products on the other. Third, the meta-analysis compares and contrasts the antecedents of two dimensions of service innovation performance (i.e., commercial success and strategic competitive advantage). Previous meta-analyses treated these two dependent variables collectively, which falls short of identifying issues that may affect management decisions when faced with different objectives. Additionally, this research investigates the effect of several other moderators (i.e., culture, unit of analysis, journal quality, and year of publication) on the relationships between the antecedents and service innovation performance. The results are discussed in relation to their implications for research and managerial practice