A Hilton-Milner theorem for vector spaces

We show for k = 2 that if q = 3 and n = 2k + 1, or q = 2 and n = 2k + 2, then any intersecting family F of k-subspaces of an n-dimensional vector space over GF(q) with nF¿F F = 0 has size at most (formula). This bound is sharp as is shown by Hilton-Milner type families. As an application of this result, we determine the chromatic number of the corresponding q-Kneser graphs

Chromatic number, clique subdivisions, and the conjectures of Haj\'os and Erd\H{o}s-Fajtlowicz

For a graph $G$, let $\chi(G)$ denote its chromatic number and $\sigma(G)$ denote the order of the largest clique subdivision in $G$. Let H(n) be the maximum of $\chi(G)/\sigma(G)$ over all $n$-vertex graphs $G$. A famous conjecture of Haj\'os from 1961 states that $\sigma(G) \geq \chi(G)$ for every graph $G$. That is, $H(n) \leq 1$ for all positive integers $n$. This conjecture was disproved by Catlin in 1979. Erd\H{o}s and Fajtlowicz further showed by considering a random graph that $H(n) \geq cn^{1/2}/\log n$ for some absolute constant $c>0$. In 1981 they conjectured that this bound is tight up to a constant factor in that there is some absolute constant $C$ such that $\chi(G)/\sigma(G) \leq Cn^{1/2}/\log n$ for all $n$-vertex graphs $G$. In this paper we prove the Erd\H{o}s-Fajtlowicz conjecture. The main ingredient in our proof, which might be of independent interest, is an estimate on the order of the largest clique subdivision which one can find in every graph on $n$ vertices with independence number $\alpha$.Comment: 14 page

Where Are My Intelligent Assistant's Mistakes? A Systematic Testing Approach

Intelligent assistants are handling increasingly critical tasks, but until now, end users have had no way to systematically assess where their assistants make mistakes. For some intelligent assistants, this is a serious problem: if the assistant is doing work that is important, such as assisting with qualitative research or monitoring an elderly parent’s safety, the user may pay a high cost for unnoticed mistakes. This paper addresses the problem with WYSIWYT/ML (What You See Is What You Test for Machine Learning), a human/computer partnership that enables end users to systematically test intelligent assistants. Our empirical evaluation shows that WYSIWYT/ML helped end users find assistants’ mistakes significantly more effectively than ad hoc testing. Not only did it allow users to assess an assistant’s work on an average of 117 predictions in only 10 minutes, it also scaled to a much larger data set, assessing an assistant’s work on 623 out of 1,448 predictions using only the users’ original 10 minutes’ testing effort

Optimization of Ex Vivo Machine Perfusion and Transplantation of Vascularized Composite Allografts

Background: Machine perfusion is gaining interest as an efficient method of tissue preservation of Vascularized Composite Allografts (VCA). The aim of this study was to develop a protocol for ex vivo subnormothermic oxygenated machine perfusion (SNMP) on rodent hindlimbs and to validate our protocol in a heterotopic hindlimb transplant model. Methods: In this optimization study we compared three different solutions during 6 h of SNMP ( n = 4 per group). Ten control limbs were stored in a preservation solution on Static Cold Storage [SCS]). During SNMP we monitored arterial flowrate, lactate levels, and edema. After SNMP, muscle biopsies were taken for histology examination, and energy charge analysis. We validated the best perfusion protocol in a heterotopic limb transplantation model with 30-d follow up ( n = 13). As controls, we transplanted untreated limbs ( n = 5) and hindlimbs preserved with either 6 or 24 h of SCS ( n = 4 and n = 5). Results: During SNMP, arterial outflow increased, and lactate clearance decreased in all groups. Total edema was significantly lower in the HBOC-201 group compared to the BSA group ( P = 0.005), 4.9 (4.3-6.1) versus 48.8 (39.1-53.2) percentage, but not to the BSA + PEG group ( P = 0.19). Energy charge levels of SCS controls decreased 4-fold compared to limbs perfused with acellular oxygen carrier HBOC-201, 0.10 (0.07-0.17) versus 0.46 (0.42-0.49) respectively ( P = 0.002). Conclusions: Six hours ex vivo SNMP of rodent hindlimbs using an acellular oxygen carrier HBOC-201 results in superior tissue preservation compared to conventional SCS. (c) 2021 Elsevier Inc. All rights reserved

Asymptotic bounds for the sizes of constant dimension codes and an improved lower bound

We study asymptotic lower and upper bounds for the sizes of constant dimension codes with respect to the subspace or injection distance, which is used in random linear network coding. In this context we review known upper bounds and show relations between them. A slightly improved version of the so-called linkage construction is presented which is e.g. used to construct constant dimension codes with subspace distance $d=4$, dimension $k=3$ of the codewords for all field sizes $q$, and sufficiently large dimensions $v$ of the ambient space, that exceed the MRD bound, for codes containing a lifted MRD code, by Etzion and Silberstein.Comment: 30 pages, 3 table

Small ball probability, Inverse theorems, and applications

Let $\xi$ be a real random variable with mean zero and variance one and $A={a_1,...,a_n}$ be a multi-set in $\R^d$. The random sum $$S_A := a_1 \xi_1 + ... + a_n \xi_n$$ where $\xi_i$ are iid copies of $\xi$ is of fundamental importance in probability and its applications. We discuss the small ball problem, the aim of which is to estimate the maximum probability that $S_A$ belongs to a ball with given small radius, following the discovery made by Littlewood-Offord and Erdos almost 70 years ago. We will mainly focus on recent developments that characterize the structure of those sets $A$ where the small ball probability is relatively large. Applications of these results include full solutions or significant progresses of many open problems in different areas.Comment: 47 page

Determination of the Michel Parameters rho, xi, and delta in tau-Lepton Decays with tau --> rho nu Tags

Using the ARGUS detector at the $e^+ e^-$ storage ring DORIS II, we have measured the Michel parameters $\rho$, $\xi$, and $\xi\delta$ for $\tau^{\pm}\to l^{\pm} \nu\bar\nu$ decays in $\tau$-pair events produced at center of mass energies in the region of the $\Upsilon$ resonances. Using $\tau^\mp \to \rho^\mp \nu$ as spin analyzing tags, we find $\rho_{e}=0.68\pm 0.04 \pm 0.08$, $\xi_{e}= 1.12 \pm 0.20 \pm 0.09$, $\xi\delta_{e}= 0.57 \pm 0.14 \pm 0.07$, $\rho_{\mu}= 0.69 \pm 0.06 \pm 0.08$, $\xi_{\mu}= 1.25 \pm 0.27 \pm 0.14$ and $\xi\delta_{\mu}= 0.72 \pm 0.18 \pm 0.10$. In addition, we report the combined ARGUS results on $\rho$, $\xi$, and $\xi\delta$ using this work und previous measurements.Comment: 10 pages, well formatted postscript can be found at http://pktw06.phy.tu-dresden.de/iktp/pub/desy97-194.p

Understanding Face and Shame: A Servant-Leadership and Face Management Model

Clergy can have a negative impact on churches and other individuals when they knowingly or unknowingly attempt to save face, that is, try to protect their standing or reputation. The desire to gain face and the fear of losing face and feeling ashamed will likely permeate clergy’s decision-making processes without even being noticed. This study explores the essence of face and face management and the relationship between face management and two characteristics of servant-leadership—awareness and healing—in both Chinese and American churches through the methodology of hermeneutic phenomenology. Prior to this study, to my knowledge, no hermeneutic phenomenological research of face management has been conducted in a church setting. Through a review of the literature, four areas are explored: face and shame, face management, servant-leadership, and face, shame, and face management within the church. This study obtained approval from the Institutional Review Board and informed consent from the participants. Three Chinese and three American Christian ministers were chosen to complete a question sheet and participate in two semi-structured interview sessions. A first cycle of open coding and second cycle of pattern coding were used during data analysis. Face experiences are discussed in light of eight major themes: body, triggers, becoming, face concepts, strategies, emotions, servant-leadership, and the church. Findings from the study help build a servant-leadership and face management model, which can offer an anchored approach for clergy and pastoral counselors to address face and shame and to develop therapeutic interventions

The need for illness

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45466/1/11089_2005_Article_BF01845887.pd