Almost all trees are almost graceful

The Graceful Tree Conjecture of Rosa from 1967 asserts that the vertices of each tree T of order n can be injectively labeled by using the numbers {1,2,…,n} in such a way that the absolute differences induced on the edges are pairwise distinct. We prove the following relaxation of the conjecture for each γ>0 and for all n>n 0(γ). Suppose that (i) the maximum degree of T is bounded by (Formula presented.)), and (ii) the vertex labels are chosen from the set {1,2,…,⌈(1+γ)n⌉}. Then there is an injective labeling of V(T) such that the absolute differences on the edges are pairwise distinct. In particular, asymptotically almost all trees on n vertices admit such a labeling. The proof proceeds by showing that a certain very natural randomized algorithm produces a desired labeling with high probability

Slow Molecules Produced by Photodissociation

A simple method to control molecular translation with a chemical reaction is demonstrated. Slow NO molecules have been produced by partially canceling the molecular beam velocity of NO$_2$ with the recoil velocity of the NO photofragment. The NO$_2$ molecules were photodissociated using a UV laser pulse polarized parallel to the molecular beam. The spatial profiles of NO molecules showed two peaks corresponding to decelerated and accelerated molecules, in agreement with theoretical prediction. A significant portion of the decelerated NO molecules stayed around the initial dissociation positions even several hundred nanoseconds after their production.Comment: 17 pages, 4 figure

First-In-Human Study in Cancer Patients Establishing the Feasibility of Oxygen Measurements in Tumors Using Electron Paramagnetic Resonance With the OxyChip

Objective: The overall objective of this clinical study was to validate an implantable oxygen sensor, called the ‘OxyChip’, as a clinically feasible technology that would allow individualized tumor-oxygen assessments in cancer patients prior to and during hypoxia-modification interventions such as hyperoxygen breathing. Methods: Patients with any solid tumor at ≤3-cm depth from the skin-surface scheduled to undergo surgical resection (with or without neoadjuvant therapy) were considered eligible for the study. The OxyChip was implanted in the tumor and subsequently removed during standard-of-care surgery. Partial pressure of oxygen (pO2) at the implant location was assessed using electron paramagnetic resonance (EPR) oximetry. Results: Twenty-three cancer patients underwent OxyChip implantation in their tumors. Six patients received neoadjuvant therapy while the OxyChip was implanted. Median implant duration was 30 days (range 4–128 days). Forty-five successful oxygen measurements were made in 15 patients. Baseline pO2 values were variable with overall median 15.7 mmHg (range 0.6–73.1 mmHg); 33% of the values were below 10 mmHg. After hyperoxygenation, the overall median pO2 was 31.8 mmHg (range 1.5–144.6 mmHg). In 83% of the measurements, there was a statistically significant (p ≤ 0.05) response to hyperoxygenation. Conclusions: Measurement of baseline pO2 and response to hyperoxygenation using EPR oximetry with the OxyChip is clinically feasible in a variety of tumor types. Tumor oxygen at baseline differed significantly among patients. Although most tumors responded to a hyperoxygenation intervention, some were non-responders. These data demonstrated the need for individualized assessment of tumor oxygenation in the context of planned hyperoxygenation interventions to optimize clinical outcomes

Speech Communication

Contains reports on five research projects.C.J. Lebel FellowshipNational Institutes of Health (Grant 5 T32 NS07040)National Institutes of Health (Grant 5 R01 NS04332)National Science Foundation (Grant 1ST 80-17599)U.S. Navy - Naval Electronic Systems Command Contract (N00039-85-C-0254)U.S. Navy - Naval Electronic Systems Command Contract (N00039-85-C-0341)U.S. Navy - Naval Electronic Systems Command Contract (N00039-85-C-0290

Speech Communication

Contains reports on five research projects.C.J. Lebel FellowshipNational Institutes of Health (Grant 5 T32 NSO7040)National Institutes of Health (Grant 5 R01 NS04332)National Institutes of Health (Grant 5 R01 NS21183)National Institutes of Health (Grant 5 P01 NS13126)National Institutes of Health (Grant 1 PO1-NS23734)National Science Foundation (Grant BNS 8418733)U.S. Navy - Naval Electronic Systems Command (Contract N00039-85-C-0254)U.S. Navy - Naval Electronic Systems Command (Contract N00039-85-C-0341)U.S. Navy - Naval Electronic Systems Command (Contract N00039-85-C-0290)National Institutes of Health (Grant RO1-NS21183), subcontract with Boston UniversityNational Institutes of Health (Grant 1 PO1-NS23734), subcontract with the Massachusetts Eye and Ear Infirmar

Yet Another User Input Method: Accelerometer Assisted Single Key Input

In this paper we present YAUIM - yet another user input method. YAUIM is an alternative user input mechanism to the conventional keyboard, mouse, and touch screen inputs. It utilizes the embedded accelerometer to detect device movements and tilt positions to enable user inputs. Accelerometers embedded in devices have been used to identify meaningful combinations of movements for gaming and small mobile devices for limited user input. Our goal is to design a fully functioning mechanism using only a single key along with accelerometer assisted positioning to emulate the computer keyboard and mouse functions. We propose to use the single key click to record a valid user input. We design a finite state automaton to combine two consecutive tilt positions to represent characters. We integrate a user specific vocabulary hinting system to improve the word input speed. YAUIM can serve as an innovative computer user input mechanism for regular desktop computers, small mobile devices, and special purpose applications

Tilt-Click: One-Handed Eyes-Free Numeric and Symbol Input for Calculator Applications

Tilt operations with audio feedback can enable data input using handheld device, single handed and eyes free. This paper presents a prototype using 5 tilt positions for numeric and symbol input for calculator applications. Two tilt positions are mapped into a single digit or one operation symbol. Users click one physical key to indicate a tilt position and hear audio feedback. Controlled experiments showed that the tilt-click input technique is feasible and promising for small mobile devices