The Upper Limit on Rates of Proton Transfer

The Bronsted plot for hydrolysis of diphenyldiazomethane by carboxylic acids is smooth but curved, approaching an asymptotic limit below 10 mo1-1 dm3 s-1• Regardless of the details of the theory used, such a limit requires that the transition state is approached via a state (or virtual state) substantially (- 70 kJ mol-1) above the starting state in free energy, but still having an intact bond from H+ to its original conjugate base. Such a state has been called a reaction complex,6 and is thought to be analogous to the intimate ion pair of solvolysis reactions

How Much Does Attention Actually Attend? Questioning the Importance of Attention in Pretrained Transformers

The attention mechanism is considered the backbone of the widely-used Transformer architecture. It contextualizes the input by computing input-specific attention matrices. We find that this mechanism, while powerful and elegant, is not as important as typically thought for pretrained language models. We introduce PAPA, a new probing method that replaces the input-dependent attention matrices with constant ones -- the average attention weights over multiple inputs. We use PAPA to analyze several established pretrained Transformers on six downstream tasks. We find that without any input-dependent attention, all models achieve competitive performance -- an average relative drop of only 8% from the probing baseline. Further, little or no performance drop is observed when replacing half of the input-dependent attention matrices with constant (input-independent) ones. Interestingly, we show that better-performing models lose more from applying our method than weaker models, suggesting that the utilization of the input-dependent attention mechanism might be a factor in their success. Our results motivate research on simpler alternatives to input-dependent attention, as well as on methods for better utilization of this mechanism in the Transformer architecture.Comment: Findings of EMNLP 202

Individual and collective stock dynamics: intra-day seasonalities

We establish several new stylised facts concerning the intra-day seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks. Somewhat paradoxically, the kurtosis (a measure of volatility surprises) reaches a minimum at the open of the market, when the volatility is at its peak. We confirm that the dispersion kurtosis is a markedly decreasing function of the index return. This means that during large market swings, the idiosyncratic component of the stock dynamics becomes sub-dominant. In a nutshell, early hours of trading are dominated by idiosyncratic or sector specific effects with little surprises, whereas the influence of the market factor increases throughout the day, and surprises become more frequent.Comment: 9 pages, 7 figure

Distribution of shortest cycle lengths in random networks

We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to configuration model networks, for which analytical results for the DSPL were obtained before. We first calculate the fraction of nodes in the network which reside on at least one cycle. Conditioning on being on a cycle, we provide the DSCL over ensembles of configuration model networks with degree distributions which follow a Poisson distribution (Erdos-R\'enyi network), degenerate distribution (random regular graph) and a power-law distribution (scale-free network). The mean and variance of the DSCL are calculated. The analytical results are found to be in very good agreement with the results of computer simulations.Comment: 44 pages, 11 figure

Temporal pattern of C1q deposition after transient focal cerebral ischemia

Recent studies have focused on elucidating the contribution of individual complement proteins to post-ischemic cellular injury. As the timing of complement activation and deposition after cerebral ischemia is not well understood, our study investigates the temporal pattern of C1q accumulation after experimental murine stroke. Brains were harvested from mice subjected to transient focal cerebral ischemia at 3, 6, 12, and 24 hr post reperfusion. Western blotting and light microscopy were employed to determine the temporal course of C1q protein accumulation and correlate this sequence with infarct evolution observed with TTC staining. Confocal microscopy was utilized to further characterize the cellular localization and characteristics of C1q deposition. Western Blot analysis showed that C1q protein begins to accumulate in the ischemic hemisphere between 3 and 6 hr post-ischemia. Light microscopy confirmed these findings, showing concurrent C1q protein staining of neurons. Confocal microscopy demonstrated co-localization of C1q protein with neuronal cell bodies as well as necrotic cellular debris. These experiments demonstrate the accumulation of C1q protein on neurons during the period of greatest infarct evolution. This data provides information regarding the optimal time window during which a potentially neuroprotective anti-C1q strategy is most likely to achieve therapeutic success. © 2006 Wiley-Liss, Inc.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50651/1/20775_ftp.pd

Overground walking speed changes when subjected to body weight support conditions for nonimpaired and post stroke individuals

<p>Abstract</p> <p>Background</p> <p>Previous research has shown that body weight support (BWS) has the potential to improve gait speed for individuals post-stroke. However, body weight support also reduces the optimal walking speed at which energy use is minimized over the gait cycle indicating that BWS should reduce walking speed capability.</p> <p>Methods</p> <p>Nonimpaired subjects and subjects post-stroke walked at a self-selected speed over a 15 m walkway. Body weight support (BWS) was provided to subjects at 0%, 10%, 20%, 30%, and 40% of the subject's weight while they walked overground using a robotic body weight support system. Gait speed, cadence, and average step length were calculated for each subject using recorded data on their time to walk 10 m and the number of steps taken.</p> <p>Results</p> <p>When subjected to greater levels of BWS, self-selected walking speed decreased for the nonimpaired subjects. However, subjects post-stroke showed an average increase of 17% in self-selected walking speed when subjected to some level of BWS compared to the 0% BWS condition. Most subjects showed this increase at the 10% BWS level. Gait speed increases corresponded to an increase in step length, but not cadence.</p> <p>Conclusions</p> <p>The BWS training environment results in decreased self-selected walking speed in nonimpaired individuals, however self-selected overground walking speed is facilitated when provided with a small percentage of body weight support for people post-stroke.</p

Abnormal joint torque patterns exhibited by chronic stroke subjects while walking with a prescribed physiological gait pattern

<p>Abstract</p> <p>Background</p> <p>It is well documented that individuals with chronic stroke often exhibit considerable gait impairments that significantly impact their quality of life. While stroke subjects often walk asymmetrically, we sought to investigate whether prescribing near normal physiological gait patterns with the use of the Lokomat robotic gait-orthosis could help ameliorate asymmetries in gait, specifically, promote similar ankle, knee, and hip joint torques in both lower extremities. We hypothesized that hemiparetic stroke subjects would demonstrate significant differences in total joint torques in both the frontal and sagittal planes compared to non-disabled subjects despite walking under normal gait kinematic trajectories.</p> <p>Methods</p> <p>A motion analysis system was used to track the kinematic patterns of the pelvis and legs of 10 chronic hemiparetic stroke subjects and 5 age matched controls as they walked in the Lokomat. The subject's legs were attached to the Lokomat using instrumented shank and thigh cuffs while instrumented footlifters were applied to the impaired foot of stroke subjects to aid with foot clearance during swing. With minimal body-weight support, subjects walked at 2.5 km/hr on an instrumented treadmill capable of measuring ground reaction forces. Through a custom inverse dynamics model, the ankle, knee, and hip joint torques were calculated in both the frontal and sagittal planes. A single factor ANOVA was used to investigate differences in joint torques between control, unimpaired, and impaired legs at various points in the gait cycle.</p> <p>Results</p> <p>While the kinematic patterns of the stroke subjects were quite similar to those of the control subjects, the kinetic patterns were very different. During stance phase, the unimpaired limb of stroke subjects produced greater hip extension and knee flexion torques than the control group. At pre-swing, stroke subjects inappropriately extended their impaired knee, while during swing they tended to abduct their impaired leg, both being typical abnormal torque synergy patterns common to stroke gait.</p> <p>Conclusion</p> <p>Despite the Lokomat guiding stroke subjects through physiologically symmetric kinematic gait patterns, abnormal asymmetric joint torque patterns are still generated. These differences from the control group are characteristic of the hip hike and circumduction strategy employed by stroke subjects.</p