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WPLI had more limitations as a measure for long-term data collections and across subjects than WPLIS because of its sensitivity to a robust and yet unexplored range of brain connectivity dynamics. This work represents a logical step towards implementation of EEG-based brain imaging in real-world settings with on-line artifact removal. One alternative approach for reducing EEG artifacts has been to use machine learning techniques such as a neural networks [10] to extract the important signal.

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The findings are an important step toward developing a computational methodology to analyze EEG activity while humans interact in a real-world environment. High-density electroencephalography (EEG) with active electrodes allows for monitoring of electrocortical dynamics during human walking but movement artifacts have the potential to dominate the signal. One potential method for recovering cognitive brain dynamics in the presence of gait-related artifact is the Weighted Phase Lag Index. Within the Aporia platform, calculating PSI is straightforward and intuitive.

• Population stability index (PSI) is a statistical measure with a basis in information theory that quantifies the difference between one probability distribution from a reference probability distribution.
• We hypothesized that WLPI would allow us to recover a p300-like event-related potential from movement artifact contaminated EEG recorded during walking that manifested from the phase relationships among channels.
• Specifically, functional connectivity is the dynamic measured connectivity that reflects the anatomical connectivity and the underlying processes occurring in the brain at a given time.
• The findings are an important step toward developing a computational methodology to analyze EEG activity while humans interact in a real-world environment.
• Python is a powerful programming language that allows simple and flexiblerepresentations of networks as well as clear and concise expressions of networkalgorithms.

How Is PSI Used In Model Monitoring and Observability?

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Schwcizers (1993) finite-element model verified Reference Föhn.Föhns (1987) formula for . Using S’ for artificially lriggered slabs and a variation, S, with for natural avalanches, Föhn rated the combined “success” of S and S’ for discriminating between snow slopes that had and had not avalanched. S or S’ is rated successful when the index is less than 1 and the slab released, or is greater than 1.5 when the slab did not release.

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Experimental factors affecting the results of shear-frame tests have been analyzed by Reference Perla and Beck.Perla and Beck (1983) and Reference JamiesonJamieson (1995, p. 65–106). Compare the numbers above with the average stock mutual fund (on an asset-weighted basis), which charged 0.44 percent, or the average stock ETF, which charged 0.16 percent. While the ETF expense ratio is the same in each case, the cost for mutual funds generally is higher.

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A) WPLI averages taken over 10 distinct 30 s intervals to highlight the time varying nature of the WPLI event-locked response. The first 30 s of the trial were averaged in interval 1 and the last 30 seconds in interval 10. Red vertical lines indicate the onset of the oddball stimulus in each interval. B,C) Channel pair WPLI responses for Stable Index selected intervals and over all time demonstrating the variability of WPLI responses across subjects. We performed a principle components analysis (PCA), using MATLAB’s built in PCA function, on the channel pairs to achieve two goals. First, we wanted to extract the primary underlying event-locked response in the WPLIS brain network.

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Teams rely on changes in prediction and feature distributions as a proxy for performance changes. PSI was picked up by the finance industry as a key metric used to measure feature drift and is one of the more stable and useful drift metrics. Figure 3 is limited to the first two minutes (~25%) of the trial for the subject. The same subject’s WPLI response, when viewed across the whole time period as shown in Figure 4a. In addition, the timings of distinct WPLI deflections, were variable across subjects (Figure 4b,c).

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This mathematical relationship enables semantic search, where a user provides query terms and LlamaIndex can locate text that is related to the meaning of the query terms rather than simple keyword matching. This is a big part of how Retrieval-Augmented Generation works, and how LLMs function in general. Matplotlib was created by neurobiologist John Hunter to work with EEGdata. It grew to be used and developed by many people in manydifferent fields. John’s goal was that Matplotlib make easy things easyand hard things possible. Although we endeavor to provide accurate and timely information, there can be no guarantee that such information is accurate as of the date it is received or that it will continue to be accurate in the future.

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Incorporating ski penetration and the proposed normal load adjustment into the formula for S results in SK which substantially reduces the proportion of false stable predictions for slabs overlying persistent weak layers. To test the potential of WPLI for the on-line assessment of cognitive dynamics, we collected EEG data from healthy human subjects standing and walking while engaged in a visual oddball discrimination task. The visual oddball discrimination task is an extremely well-studied [20, 21] paradigm involving a subject viewing presentations of two stimuli; a ‘standard’ that occurs often, and an ‘oddball’ that occurs infrequently. The presentation of this oddball is known to create an event-related potential (ERP) at about 300 milliseconds after presentation of the oddball (p300), as measured by EEG. We hypothesized that WLPI would allow us to recover a p300-like event-related potential from movement artifact contaminated EEG recorded during walking that manifested from the phase relationships among channels.

The slab thickness in the start zone, h, is plotted against Sk in Figure 8 for the same 83 persistent (square symbols) and 32 non-persistent slabs (round symbols) used to assess S in the previous section. Within the unstable range of the persistent slabs and 63% (152 /24) of the non-persistent slabs failed. Within the band of transitional stability, of the persistent slab and none (0/5) of the non-persistent slabs failed. We demonstrated that WPLIS can be used to recover event-locked cognitive activity from artifact-contaminated EEG recorded during a walking task.

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In addition, the application of measures such as mean path length, clustering coefficients, and betweeness centrality could help researchers further understand connectivity changes within and between tasks [28, 31, 32]. Lastly, a comparison to the debiased WPLI may advance the results presented here [15]. There are a number of areas where this methodology can be expanded to provide additional insight into underlying cognitive activity. Most importantly, the time-varying nature of WPLI dynamics should be studied in more detail. Figure 4 exhibits a complex and variable WPLI response across subjects and time.

Estimating Ski Penetration from Slab Density

• 248-channel EEG was recorded as eight subjects performed a visual oddball discrimination and response task during standing and walking (0.8 or 1.2 m/s) on a treadmill.
• Investors should avoid timing the market, that is, jumping in and out of the market to capture gains and dodge losses.
• In our credit-scoring example, PSI is pivotal in identifying discrepancies between the credit-scoring model’s assumptions and the actual data.
• Argentina, plagued by economic crisis, and Venezuela, hit by coup and counter-coup, score lowest.
• Panel (g) shows the voltage amplitude response locked to left heel-strike and how significant the walking artifact is.
• WPLI measures the interaction between channel pairs and quantifies the dynamic interaction between them, reflecting the functional connectivity between brain regions.
• The artifacts from this event are many orders of magnitude larger than the voltage changes due to a cognitive response.

These decreases in the proportion of slab failures for increasing values of a stability index are measures of the effectiveness of the index. Shear-frame stability indices have been used to assess the stability of snow slopes for many years (Reference RochRoch, 1966a; Reference RochSchleiss and Schlciss, 1970). When combined with other forecasting variables such as previous avalanches, snowpack observations and meteorological data, they have the potential to improve avalanche forecasting (Reference JamiesonJamieson, 1995, p. 195–238).

• Where ρ is the average slab density, g is the acceleration due to gravity, h is the slab thickness measured vertically and is the slope inclination.
• The BTI publishes two rankings, the Status Index and the Governance Index, both of which are based on in-depth assessments of 137 countries.
• To do this, you must register on Stable Index and immediately use the tools to choose the right trades for you in trading.
• According to the index, cost of freight and labor have been the predominant causes of stress in the supply chain, accounting for the majority of the variability in operations performance.
• The points for seven dry-slab avalanches that were skier-triggered from more than 50 m away from the avalanche are marked with a surrounding square in Figure 8.

Principal Component Analysis of WPLIS Event-Locked Response

It demonstrates the four conditions in this EEG study along with the conventional (left) and WPLI (right) processing methods. Notice the time arrows along the left side demonstrating which methods can be computed on-line and which must be done post-hoc. We generated a topographic map showing the extent to which each channel pair contributed to the first principal component (PC) of the WPLIS response. This was done by summing, for each channel of a channel pair, the positive contributions (PC loading) to the first PC.

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• The lifted index should be used cautiously as it only shows instability at one point in the atmopshere, not the measure of instability across the whole atmospheric region (CAPE).
• Thanks to your efforts and skills, as well as the correct use of capital, it is possible to achieve incredible results.
• When the maximum ski penetration exceeds the slab thickness is defined to be 0, since the weak layer will be highly stressed when the skis approach the weak layer during the skier’s up and down motion.
• The key task of an investor remains to combine the opportunities on Stable Index to maximize the results of your investment.
• PSI is also utilized to ensure that input or output data in production doesn’t drastically change from a baseline.
• WPLI, in particular, is a functional connectivity measure that was designed to ignore non-brain sources of activity.
• Channel-pair WPLIS responses were averaged across subjects and then sorted by correlation to the mean.

Stock market returns have been above their historical averages over the past five- and 10-year periods and several new all-time highs have been reached in 2024. This may give investors pause about committing new money, but financial advisors say investing at all-time highs doesn’t lead to poor long-term returns. If you’re buying a stock index fund or almost any broadly diversified stock fund such as one based on the S&P 500, it can be a good time to buy if you’re prepared to hold it for the long term. That’s because the market tends to rise over time, as the economy grows and corporate profits increase.

Features¶

In the initial stages of model building, the development dataset is used for data exploration, feature engineering, and model training, so that the model can capture the underlying patterns and relationships in the data. When calculating PSI, we use the development dataset as a reference or baseline. PSI evaluates model stability by comparing category distributions in development and validation populations. Understanding PSI’s mathematical essence empowers analysts to effectively evaluate and maintain their models’ performance over time. A significant surge in PSI implies a substantial shift in the fundamental data, which makes the credit-scoring model less reliable.

Weighted Phase Lag Index Stability

We use an independent dataset that is not used during the model training process—the validation dataset—to assess the performance of the model on unseen data to ensure that the model generalizes well to new instances. The Population Stability Index (PSI) is a statistical measure rooted in information theory, assessing the distinction between a given probability distribution and a reference distribution. ArXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Breaking feedback loops and vicious cycles requires comprehensive, holistic responses. As maritime security strategies become more comprehensive and holistic, so too must our attempts to measure progress.

Second, we sought to map the spatial distribution of the channel pairs that contributed most highly to the event-locked WPLIS response. The error for all WPLIS was calculated as the standard error across all eight subjects. WPLIS changes were calculated in reference to the baseline by averaging the 0.5 s epoch prior to oddball presentation. Then, the minimum WPLIS value was extracted for the 1.5 s epoch following the oddball presentation. The error for that minimum value was then used to calculate z-scores and p-values for the minimum. Subjects stood and walked (0.8 m/s), on a treadmill while we recorded 248-channel electroencephalography at 512 Hz (ActiveTwo, BioSemi, Amsterdam, The Netherlands).

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Channels that contributed most strongly and most often (as a part of various channel pairs) to the first PC, had the highest cumulative loading and the warmest topographic map color. Hungary is the most stable emerging economy of those measured by an index produced by Lehman Brothers and Eurasia Group, a firm that analyses political risk. The index assesses a country’s ability to withstand and avoid generating crises.

This mutual fund began trading in 2000 and has a strong record over the last five and ten years. Schwab is especially noted for its focus on making investor-friendly products, as evidenced by this fund’s razor-thin expense ratio. This mutual fund has a strong record dating back to 1997, and it’s sponsored by Charles Schwab, one of the most respected names in the industry. This ETF began trading in 2010, and it’s backed by Vanguard, one of the powerhouses of the fund industry.

To visualize the PSI, we will create a prepare_data_for_plotting method that functions similarly to the population_stability_index. Instead of calculating the PSI, this method will populate two extra columns with the percentages of each bin. To format the information so that it’s easier for people to understand, we will multiply the percentage by 100. We group the data by bins, and the number of scores in each bin is counted for both datasets. The result is stored in two separate data frames, dev_group and val_group. To craft a model, you grab a handful of marbles (the development set).

All subjects provided written informed consent prior to the experiment. The University of Michigan Internal Review Board approved the protocol and we complied with all standards defined in the Declaration of Helsinki. More detailed accounts of the data collection methods can be found in previous publications [9]. Thin-cap fibroatheroma was the strongest single predictor of future LOCE events but the risk increased significantly with the simultaneous presence of four OCT-VFs.

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However, WPLI responses that were time locked to the appearance of a visual oddball stimulus during walking were highly variable across subjects and trials. We found that a stability measure of WPLI (i.e. WPLIS) provided a more robust p300-like cognitive event during walking. In the most general sense, a stability measure of any metric will provide a more generalized measure of its dynamic properties. The stability measure used here is analogous to the Fano Factor [24], which has been expanded to generalize the inter-spike intervals of neuronal firing. WPLIS allows for the comparison and averaging of responses within sessions and between subjects.

If WPLI is a measure of the functional flow of information between two brain regions (mapped to EEG channels in this case) [15], then a low WPLIS reflects continuous and uniform flow of this information. Conversely, if WPLIS is high then WPLI is highly irregular and an unstable dynamic information flow is implied. The iSTOXX Access Metaverse Index tracks the performance of equities listed on global recognized stock exchanges that exhibit business characteristics related to the Metaverse. The index composition is reviewed semi-annually, and its constituents are weighted by free-float market capitalization, with maximum and minimum weight caps. Meteorologists use stability indices to quickly assess thesusceptibility of the atmosphere to severe weather.