On Profit-Maximizing Pricing for the Highway and Tollbooth Problems

In the \emph{tollbooth problem}, we are given a tree \bT=(V,E) with $n$ edges, and a set of $m$ customers, each of whom is interested in purchasing a path on the tree. Each customer has a fixed budget, and the objective is to price the edges of \bT such that the total revenue made by selling the paths to the customers that can afford them is maximized. An important special case of this problem, known as the \emph{highway problem}, is when \bT is restricted to be a line. For the tollbooth problem, we present a randomized $O(\log n)$-approximation, improving on the current best $O(\log m)$-approximation. We also study a special case of the tollbooth problem, when all the paths that customers are interested in purchasing go towards a fixed root of \bT. In this case, we present an algorithm that returns a $(1-\epsilon)$-approximation, for any $\epsilon > 0$, and runs in quasi-polynomial time. On the other hand, we rule out the existence of an FPTAS by showing that even for the line case, the problem is strongly NP-hard. Finally, we show that in the \emph{coupon model}, when we allow some items to be priced below zero to improve the overall profit, the problem becomes even APX-hard

One-stage Flexor Reconstruction With Anterolateral Thigh and Fascia Lata Rolls After High-Voltage Trauma: A Case Report

BACKGROUND: Electrical injuries from high-voltage power lines are unique forms of trauma that can create challenging wounds for reconstructive surgeons. Our patients, a man in his late thirties (Patient 1) and a man in his early twenties (Patient 2), both sustained upper extremity injuries after contact with a high-voltage line. METHODS: Despite minimal superficial damage, both patients required fasciotomies and debridement of the volar forearm, revealing segmental defects in most digital tendons as well as the distal median nerve. Free fasciocutaneous anterolateral thigh (ALT) flaps were harvested to ensure adequate wound coverage. Additionally, fascia lata grafts were taken from the free flap donor site and rolled into tubes to transfer available flexor digitorum superficialis proximal tendon stumps to the distal stumps of flexor digitorum profundus. The rolls were also used to bridge segmental tendon defects in flexor pollicis longus, while cadaveric nerve allografts were used to bridge the median nerve defects. RESULTS: Nine months postoperatively, Patient 1 had premorbid function with activities of daily living (ADLs), and Patient 2 required only minimal assistance with instrumental ADLs. Within a year following reconstruction, Patient 1 mostly regained range of motion in his digits with some rigidity, and Patient 2 regained full range of motion in his digits with minimal rigidity. CONCLUSIONS: These cases have demonstrated that the use of an ALT free flap combined with rolled fascia lata graft tubes may be an effective choice for reconstruction and functional restoration in cases of severe high-voltage electrical trauma

Total Reconstruction of Lower Lip and Chin Following Firework Injury Using Composite Bilateral Radial Forearm-Fascia Lata Flaps: A Case Report

BACKGROUND: Primary explosion injuries with fireworks can lead to devastating and geometrically complex facial traumas that present a challenge to the reconstructive surgeon. Our patient, a woman in her early thirties, was hit directly in her chin by a large artillery shell firework. This caused complete soft tissue loss of the lower lip and chin beyond the oral commissures, complicated further by a comminuted mandible fracture. METHODS: After external fixation, our patient underwent a 2-stage reconstruction with a novel composite flap arrangement. Soft tissue coverage and lip reconstruction were performed with opposing bilateral radial forearm free flaps. The outer flap constituted the soft tissue of the new chin and outer lower lip, whereas the inner flap composed the intraoral lining. In the second stage, portions of the inner upper lip mucosa and superior orbicularis oris muscle were flipped down as a bipedicle, axial pattern bucket-handle type flap to the lower lip to reconstruct the vermilion. A graft of fascia lata was attached to the modioli of the orbicularis oris and interpositioned beneath the vermilion flap and the radial forearms to restore static and some dynamic sphincter control. One month later, the mandibular fractures underwent open reduction and internal fixation. RESULTS: Two months after soft tissue reconstruction with no complications, our patient had satisfactory aesthetic outcomes, oral competence, and speech. CONCLUSIONS: This case has shown that use of bilateral, fascia lata-reinforced radial forearm flaps may be an effective choice for soft tissue reconstruction and oral competence restoration in cases of severe facial explosion trauma

Diapause vs. reproductive programs: transcriptional phenotypes in a keystone copepod

© The Author(s), 2021. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Lenz, P. H., Roncalli, V., Cieslak, M. C., Tarrant, A. M., Castelfranco, A. M., & Hartline, D. K. Diapause vs. reproductive programs: transcriptional phenotypes in a keystone copepod. Communications Biology, 4(1), (2021): 426, https://doi.org/10.1038/s42003-021-01946-0.Many arthropods undergo a seasonal dormancy termed “diapause” to optimize timing of reproduction in highly seasonal environments. In the North Atlantic, the copepod Calanus finmarchicus completes one to three generations annually with some individuals maturing into adults, while others interrupt their development to enter diapause. It is unknown which, why and when individuals enter the diapause program. Transcriptomic data from copepods on known programs were analyzed using dimensionality reduction of gene expression and functional analyses to identify program-specific genes and biological processes. These analyses elucidated physiological differences and established protocols that distinguish between programs. Differences in gene expression were associated with maturation of individuals on the reproductive program, while those on the diapause program showed little change over time. Only two of six filters effectively separated copepods by developmental program. The first one included all genes annotated to RNA metabolism and this was confirmed using differential gene expression analysis. The second filter identified 54 differentially expressed genes that were consistently up-regulated in individuals on the diapause program in comparison with those on the reproductive program. Annotated to oogenesis, RNA metabolism and fatty acid biosynthesis, these genes are both indicators for diapause preparation and good candidates for functional studies.This work was supported by National Science Foundation Grants (NSF) OCE-1459235 and OCE-1756767 to P.H.L., D.K.H. and AE Christie and OPP-1746087 to A.M.T

Scoring schemes of palindrome clusters for more sensitive prediction of replication origins in herpesviruses

Many empirical studies show that there are unusual clusters of palindromes, closely spaced direct and inverted repeats around the replication origins of herpesviruses. In this paper, we introduce two new scoring schemes to quantify the spatial abundance of palindromes in a genomic sequence. Based on these scoring schemes, a computational method to predict the locations of replication origins is developed. When our predictions are compared with 39 known or annotated replication origins in 19 herpesviruses, close to 80% of the replication origins are located within 2% of the genome length. A list of predicted locations of replication origins in all the known herpesviruses with complete genome sequences is reported

Aeronautics Testing Facilities Overview

No abstract availabl

Subbarrel patterns in somatosensory cortical barrels can emerge from local dynamic instabilities

Complex spatial patterning, common in the brain as well as in other biological systems, can emerge as a result of dynamic interactions that occur locally within developing structures. In the rodent somatosensory cortex, groups of neurons called "barrels" correspond to individual whiskers on the contralateral face. Barrels themselves often contain subbarrels organized into one of a few characteristic patterns. Here we demonstrate that similar patterns can be simulated by means of local growth-promoting and growth-retarding interactions within the circular domains of single barrels. The model correctly predicts that larger barrels contain more spatially complex subbarrel patterns, suggesting that the development of barrels and of the patterns within them may be understood in terms of some relatively simple dynamic processes. We also simulate the full nonlinear equations to demonstrate the predictive value of our linear analysis. Finally, we show that the pattern formation is robust with respect to the geometry of the barrel by simulating patterns on a realistically shaped barrel domain. This work shows how simple pattern forming mechanisms can explain neural wiring both qualitatively and quantitatively even in complex and irregular domains. © 2009 Ermentrout et al

2-(4,5-Dihydro-1,3-oxazol-2-yl)quinoline

The title compound, C12H10N2O, is approximately planar. The angle between the quinoline and 4,5-dihydro­oxazole ring systems is 11.91 (12)°. The mol­ecules pack into a herringbone array with no significant π–π inter­actions. The dihydro­oxazole N and O atoms are disordered over two positions, with almost equal site occupancy factors

Representation of Time-Varying Stimuli by a Network Exhibiting Oscillations on a Faster Time Scale

Sensory processing is associated with gamma frequency oscillations (30–80 Hz) in sensory cortices. This raises the question whether gamma oscillations can be directly involved in the representation of time-varying stimuli, including stimuli whose time scale is longer than a gamma cycle. We are interested in the ability of the system to reliably distinguish different stimuli while being robust to stimulus variations such as uniform time-warp. We address this issue with a dynamical model of spiking neurons and study the response to an asymmetric sawtooth input current over a range of shape parameters. These parameters describe how fast the input current rises and falls in time. Our network consists of inhibitory and excitatory populations that are sufficient for generating oscillations in the gamma range. The oscillations period is about one-third of the stimulus duration. Embedded in this network is a subpopulation of excitatory cells that respond to the sawtooth stimulus and a subpopulation of cells that respond to an onset cue. The intrinsic gamma oscillations generate a temporally sparse code for the external stimuli. In this code, an excitatory cell may fire a single spike during a gamma cycle, depending on its tuning properties and on the temporal structure of the specific input; the identity of the stimulus is coded by the list of excitatory cells that fire during each cycle. We quantify the properties of this representation in a series of simulations and show that the sparseness of the code makes it robust to uniform warping of the time scale. We find that resetting of the oscillation phase at stimulus onset is important for a reliable representation of the stimulus and that there is a tradeoff between the resolution of the neural representation of the stimulus and robustness to time-warp. Author Summary Sensory processing of time-varying stimuli, such as speech, is associated with high-frequency oscillatory cortical activity, the functional significance of which is still unknown. One possibility is that the oscillations are part of a stimulus-encoding mechanism. Here, we investigate a computational model of such a mechanism, a spiking neuronal network whose intrinsic oscillations interact with external input (waveforms simulating short speech segments in a single acoustic frequency band) to encode stimuli that extend over a time interval longer than the oscillation's period. The network implements a temporally sparse encoding, whose robustness to time warping and neuronal noise we quantify. To our knowledge, this study is the first to demonstrate that a biophysically plausible model of oscillations occurring in the processing of auditory input may generate a representation of signals that span multiple oscillation cycles.National Science Foundation (DMS-0211505); Burroughs Wellcome Fund; U.S. Air Force Office of Scientific Researc