The Epsilon Calculus and Herbrand Complexity

Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p

Crystallization of classical multi-component plasmas

We develop a method for calculating the equilibrium properties of the liquid-solid phase transition in a classical, ideal, multi-component plasma. Our method is a semi-analytic calculation that relies on extending the accurate fitting formulae available for the one-, two-, and three-component plasmas to the case of a plasma with an arbitrary number of components. We compare our results to those of Horowitz, Berry, & Brown (Phys. Rev. E, 75, 066101, 2007), who use a molecular dynamics simulation to study the chemical properties of a 17-species mixture relevant to the ocean-crust boundary of an accreting neutron star, at the point where half the mixture has solidified. Given the same initial composition as Horowitz et al., we are able to reproduce to good accuracy both the liquid and solid compositions at the half-freezing point; we find abundances for most species within 10% of the simulation values. Our method allows the phase diagram of complex mixtures to be explored more thoroughly than possible with numerical simulations. We briefly discuss the implications for the nature of the liquid-solid boundary in accreting neutron stars.Comment: 14 pages, 5 figures, submitted to Phys. Rev.

Model Atmospheres for X-ray Bursting Neutron Stars

The hydrogen and helium accreted by X-ray bursting neutron stars is periodically consumed in runaway thermonuclear reactions that cause the entire surface to glow brightly in X-rays for a few seconds. With models of the emission, the mass and radius of the neutron star can be inferred from the observations. By simultaneously probing neutron star masses and radii, X-ray bursts are one of the strongest diagnostics of the nature of matter at extremely high densities. Accurate determinations of these parameters are difficult, however, due to the highly non-ideal nature of the atmospheres where X-ray bursts occur. Observations from X-ray telescopes such as RXTE and NuStar can potentially place strong constraints on nuclear matter once uncertainties in atmosphere models have been reduced. Here we discuss current progress on modeling atmospheres of X-ray bursting neutron stars and some of the challenges still to be overcome.Comment: 25 pages, 14 figure

Successful Cessation Programs that Reduce Comorbidity May Explain Surprisingly Low Smoking Rates Among Hospitalized COVID-19 Patients

A recent, non-peer-reviewed meta-analysis suggests that smoking may reduce the risk of hospitalization with COVID-19 because the prevalence of smoking among hospitalized COVID-19 is less than that of the general population. However, there are alternative explanations for this phenomena based on (1) the failure to report, or accurately record, smoking history during emergency hospital admissions and (2) a pre-disposition to avoid smoking among COVID-19 patients with tobacco-related comorbidities (a type of “reverse” causation). For example, urine testing of hospitalized patients in Australia for cotinine showed that smokers were under-counted by 37% because incoming patients failed to inform staff about their smoking behavior. Face-to-face interviews can introduce bias into the responses to attitudinal and behavioral questions not present in the self-completion interviews typically used to measure smoking prevalence in the general population. Subjects in face-to-face interviews may be unwilling to admit socially undesirable behavior and attitudes under direct questioning. Reverse causation may also contribute to the difference between smoking prevalence in the COVID-19 and general population. Patients hospitalized with COVID-19 may be simply less prone to use tobacco than the general population. A potentially robust “reverse causation” hypothesis for reduced prevalence of smokers in the COVID-19 population is the enrichment of patients in that population with serious comorbidities that motivates them to quit smoking. We judge that this “smoking cessation” mechanism may account for a significant fraction of the reduced prevalence of smokers in the COVID-19 population. Testing this hypothesis will require a focused research program

Verwey transition in Fe3_{3}O4_{4} at high pressure: quantum critical behavior at the onset of metallization

We provide evidence for the existence of a {\em quantum critical point} at the metallization of magnetite Fe$_{3}$O$_{4}$ at an applied pressure of $p_{c} \approx 8$ GPa. We show that the present ac magnetic susceptibility data support earlier resistivity data. The Verwey temperature scales with pressure $T_{V}\sim (1-p/p_{c})^{\nu}$, with $\nu\sim 1/3$. The resistivity data shows a temperature dependence $\rho(T)=\rho_{0}+AT^{n}$, with $n\simeq 3$ above and 2.5 at the critical pressure, respectively. This difference in $n$ with pressure is a sign of critical behavior at $p_{c}$. The magnetic susceptibility is smooth near the critical pressure, both at the Verwey transition and near the ferroelectric anomaly. A comparison with the critical behavior observed in the Mott-Hubbard and related systems is made.Comment: 5 pages, 5 figure

Takeuti's Well-Ordering Proof: Finitistically Fine?

If it could be shown that one of Gentzen's consistency proofs for pure number theory could be shown to be finitistically acceptable, an important part of Hilbert's program would be vindicated. This paper focuses on whether the transfinite induction on ordinal notations needed for Gentzen's second proof can be finitistically justified. In particular, the focus is on Takeuti's purportedly finitistically acceptable proof of the well-ordering of ordinal notations in Cantor normal form. The paper begins with a historically informed discussion of finitism and its limits, before introducing Gentzen and Takeuti's respective proofs. The rest of the paper is dedicated to investigating the finitistic acceptability of Takeuti's proof, including a small but important fix to that proof. That discussion strongly suggests that there is a philosophically interesting finitist standpoint that Takeuti's proof, and therefore Gentzen's proof, conforms to

Flexible Session Management in a Distributed Environment

Many secure communication libraries used by distributed systems, such as SSL, TLS, and Kerberos, fail to make a clear distinction between the authentication, session, and communication layers. In this paper we introduce CEDAR, the secure communication library used by the Condor High Throughput Computing software, and present the advantages to a distributed computing system resulting from CEDAR's separation of these layers. Regardless of the authentication method used, CEDAR establishes a secure session key, which has the flexibility to be used for multiple capabilities. We demonstrate how a layered approach to security sessions can avoid round-trips and latency inherent in network authentication. The creation of a distinct session management layer allows for optimizations to improve scalability by way of delegating sessions to other components in the system. This session delegation creates a chain of trust that reduces the overhead of establishing secure connections and enables centralized enforcement of system-wide security policies. Additionally, secure channels based upon UDP datagrams are often overlooked by existing libraries; we show how CEDAR's structure accommodates this as well. As an example of the utility of this work, we show how the use of delegated security sessions and other techniques inherent in CEDAR's architecture enables US CMS to meet their scalability requirements in deploying Condor over large-scale, wide-area grid systems

Graph Distillation for Action Detection with Privileged Modalities

We propose a technique that tackles action detection in multimodal videos under a realistic and challenging condition in which only limited training data and partially observed modalities are available. Common methods in transfer learning do not take advantage of the extra modalities potentially available in the source domain. On the other hand, previous work on multimodal learning only focuses on a single domain or task and does not handle the modality discrepancy between training and testing. In this work, we propose a method termed graph distillation that incorporates rich privileged information from a large-scale multimodal dataset in the source domain, and improves the learning in the target domain where training data and modalities are scarce. We evaluate our approach on action classification and detection tasks in multimodal videos, and show that our model outperforms the state-of-the-art by a large margin on the NTU RGB+D and PKU-MMD benchmarks. The code is released at http://alan.vision/eccv18_graph/.Comment: ECCV 201

Investigating the Avoidability of Hospitalizations of Long Stay Nursing Home Residents: Opportunities for Improvement

Background and Objectives: To examine the relationship between hospital diagnoses associated with hospital transfers of long stay nursing home residents, ratings of avoidability of transfer, and RN-identified quality improvement opportunities. Research Design and Methods: Prospective clinical demonstration project, named OPTIMISTIC, with trained RNs embedded in nursing homes that performed root cause analyses for 1,931 transfers to the hospital between November 2014 and July 2016. OPTIMISTIC RNs also rated whether transfers were avoidable, identified quality improvement opportunities, and recorded hospital diagnoses. Resident characteristics were obtained from Minimum Data Set assessments. Relationships between six hospital diagnoses commonly considered "potentially avoidable" and OPTIMISTIC RN root cause analysis findings were examined. Facilities were participating in the OPTIMISTIC demonstration project designed to reduce hospital transfers during the study period. Results: Twenty-five percent of acute transfers associated with six common diagnoses were considered definitely or probably avoidable by project RNs versus 22% of transfers associated with other diagnoses. The most common quality improvement opportunity identified for transfers rated as avoidable was that the condition could have been managed safely if appropriate resources were available, a factor cited in 45% of transfers associated with any of the six diagnoses. Problems with communication among stakeholders were the most commonly noted area for improvement (48%) for transfers associated with other diagnoses. Many other areas for quality improvement were noted, including earlier detection of change in status and the need for understanding patient preferences or a palliative care plan. Discussion and Implications: Although some nursing home transfers may later be deemed potentially avoidable based on post-transfer hospital diagnosis from Medicare claims data, OPTIMISTIC nurses caring for these residents at time of transfer categorized the majority of these transfers as unavoidable irrespective of the hospital diagnosis. Multiple quality improvement opportunities were identified associated with these hospital transfers, whether the transfer was considered potentially avoidable or unavoidable