Ensemble dependence of the critical behavior of a system with long-range interaction and quenched randomness.

We propose a hybrid model governed by the Blume-Emery-Griffiths (BEG) Hamiltonian with a mean-field-like interaction, where the spins are randomly quenched such that some of them are "pure" Ising and the others admit the BEG set of states. It is found, by varying the concentration of the Ising spins, that the model displays different phase portraits in concentration-temperature parameter space, within the canonical and the microcanonical ensembles. Phenomenological indications that these portraits are rich and rather unusual are provided.

Mutual Information between Order Book Layers.

The order book is a list of all current buy or sell orders for a given financial security. The rise of electronic stock exchanges introduced a debate about the relevance of the information it encapsulates of the activity of traders. Here, we approach this topic from a theoretical perspective, estimating the amount of mutual information between order book layers, i.e., different buy/sell layers, which are aggregated by buy/sell orders. We show that (i) layers are not independent (in the sense that the mutual information is statistically larger than zero), (ii) the mutual information between layers is small (compared to the joint entropy), and (iii) the mutual information between layers increases when comparing the uppermost layers to the deepest layers analyzed (i.e., further away from the market price). Our findings, and our method for estimating mutual information, are relevant to developing trading strategies that attempt to utilize the information content of the limit order book.

Forecasting Quoted Depth With the Limit Order Book.

Liquidity plays a vital role in the financial markets, affecting a myriad of factors including stock prices, returns, and risk. In the stock market, liquidity is usually measured through the order book, which captures the orders placed by traders to buy and sell stocks at different price points. The introduction of electronic trading systems in recent years made the deeper layers of the order book more accessible to traders and thus of greater interest to researchers. This paper examines the efficacy of leveraging the deeper layers of the order book when forecasting quoted depth-a measure of liquidity-on a per-minute basis. Using Deep Feed Forward Neural Networks, we show that the deeper layers do provide additional information compared to the upper layers alone.

The effect of age and injury severity on clinical prediction rules for ambulation among individuals with spinal cord injury.

BACKGROUND CONTEXT: While several models for predicting independent ambulation early after traumatic spinal cord injury (SCI) based upon age and specific motor and sensory level findings have been published and validated, their accuracy, especially in individual American Spinal Injury Association [ASIA] Impairment Scale (AIS) classifications, has been questioned. Further, although age is widely used in prediction rules, its role and possible modifications have not been adequately evaluated until now. PURPOSE: To evaluate the predictive accuracy of existing clinical prediction rules for independent ambulation among individuals at spinal cord injury model systems (SCIMS) Centers as well as the effect of modifying the age parameter from a cutoff of 65 years to 50 years. STUDY DESIGN: Retrospective analysis of a longitudinal database. PATIENT SAMPLE: Adult individuals with traumatic SCI. OUTCOME MEASURES: The FIM locomotor score was used to assess independent walking ability at the 1-year follow-up. METHODS: In all, 639 patients were enrolled in the SCIMS database between 2011 and 2015, with complete neurological examination data within 15 days following the injury and a follow-up assessment with functional independence measure (FIM) at 1-year post injury. Two previously validated logistic regression models were evaluated for their ability to predict independent walking at 1-year post injury with participants in the SCIMS database. Area under the receiver operating curve (AUC) was calculated for the individual AIS categories and for different age groups. Prediction accuracy was also calculated for a new modified LR model (with cut-off age of 50). RESULTS: Overall AUC for each of the previous prediction models was found to be consistent with previous reports (0.919 and 0.904). AUCs for grouped AIS levels (A+D, B+C) were consistent with prior reports, moreover, prediction for individual AIS grades continued to reveal lower values. AUCs by different age categories showed a decline in prognostication accuracy with an increase in age, with statistically significant improvement of AUC when age-cut off was reduced to 50. CONCLUSIONS: We confirmed previous results that former prediction models achieve strong prognostic accuracy by combining AIS subgroups, yet prognostication of the separate AIS groups is less accurate. Further, prognostication of persons with AIS B+C, for whom a clinical prediction model has arguably greater clinical utility, is less accurate than those with AIS A+D. Our findings emphasize that age is an important factor in prognosticating ambulation following SCI. Prediction accuracy declines for older individuals compared with younger ones. To improve prediction of independent ambulation, the age of 50 years may be a better cutoff instead of age of 65.

Unusual changeover in the transition nature of local-interaction Potts models.

A combinatorial approach is used to study the critical behavior of a q-state Potts model with a round-the-face interaction. Using this approach, it is shown that the model exhibits a first order transition for q>3. A second order transition is numerically detected for q=2. Based on these findings, it is deduced that for some two-dimensional ferromagnetic Potts models with completely local interaction, there is a changeover in the transition order at a critical integer q_{c}≤3. This stands in contrast to the standard two-spin interaction Potts model where the maximal integer value for which the transition is continuous is q_{c}=4. A lower bound on the first order critical temperature is additionally derived.

Volume Prediction With Neural Networks.

Changes in intraday trading volume are integral to any algorithmic trading strategy. Accordingly, forecasting the change in trading volume is paramount to better understanding the financial markets. This paper introduces a new method to forecast the log change in trading volume, leveraging the power of Long Short Term Memory (LSTM) networks in conjunction with Support Vector Regression (SVR) and Autoregressive (AR) models. We show that LSTM contributes to a more accurate forecast, particularly when constructed as part of a hybrid model with AR. The algorithm is extended to include data about the time of day, helping the model associate the log change in trading volume with the current hour, which yields the best performance of all trials.

Ferromagnetic Potts models with multisite interaction.

We study the q-state Potts model with four-site interaction on a square lattice. Based on the asymptotic behavior of lattice animals, it is argued that when q≤4 the system exhibits a second-order phase transition and when q>4 the transition is first order. The q=4 model is borderline. We find 1/lnq to be an upper bound on T_{c}, the exact critical temperature. Using a low-temperature expansion, we show that 1/(θlnq), where θ>1 is a q-dependent geometrical term, is an improved upper bound on T_{c}. In fact, our findings support T_{c}=1/(θlnq). This expression is used to estimate the finite correlation length in first-order transition systems. These results can be extended to other lattices. Our theoretical predictions are confirmed numerically by an extensive study of the four-site interaction model using the Wang-Landau entropic sampling method for q=3,4,5. In particular, the q=4 model shows an ambiguous finite-size pseudocritical behavior.

Support vector machine-based differentiation between aggressive and chronic periodontitis using microbial profiles.

BACKGROUND: The existence of specific microbial profiles for different periodontal conditions is still a matter of debate. The aim of this study was to test the hypothesis that 40 bacterial species could be used to classify patients, utilising machine learning, into generalised chronic periodontitis (ChP), generalised aggressive periodontitis (AgP) and periodontal health (PH). METHOD: Subgingival biofilm samples were collected from patients with AgP, ChP and PH and analysed for their content of 40 bacterial species using checkerboard DNA-DNA hybridisation. Two stages of machine learning were then performed. First of all, we tested whether there was a difference between the composition of bacterial communities in PH and in disease, and then we tested whether a difference existed in the composition of bacterial communities between ChP and AgP. The data were split in each analysis to 70% train and 30% test. A support vector machine (SVM) classifier was used with a linear kernel and a Box constraint of 1. The analysis was divided into two parts. RESULTS: Overall, 435 patients (3,915 samples) were included in the analysis (PH = 53; ChP = 308; AgP = 74). The variance of the healthy samples in all principal component analysis (PCA) directions was smaller than that of the periodontally diseased samples, suggesting that PH is characterised by a uniform bacterial composition and that the bacterial composition of periodontally diseased samples is much more diverse. The relative bacterial load could distinguish between AgP and ChP. CONCLUSION: An SVC classifier using a panel of 40 bacterial species was able to distinguish between PH, AgP in young individuals and ChP.