A sharpened estimate on the pseudo-Gamma function

The pseudo-Gamma function is a key tool introduced recently by Cheng and Albeverio in the proof of \break the density hypothesis. This function is doubly symmetric, which means that it is reflectively symmetric about the real axis by the Schwarz principle, whereas it is also reflectively symmmetric about the half line where the real part of the variable is equal to $\tfrac{1}{2}$. In this article, we sharpen the estimate given in the proof of the density hypothesis for this doubly symmetric pseudo-Gamma function on the real axis near the symmetry center by taking a different approach from the way used in the density hypothesis proof directly from the definition, reducing the error caused by the fact that the difference of two pivotal parameters in the definition of the pseudo-Gamma function is much larger than the difference of the variables in this particular case.Comment: 8 pages, submitted to Journal of combinatorics and number theory, June 11, 201

Interactive Data Analysis with Next-step Natural Language Query Recommendation

Natural language interfaces (NLIs) provide users with a convenient way to interactively analyze data through natural language queries. Nevertheless, interactive data analysis is a demanding process, especially for novice data analysts. When exploring large and complex SQL databases from different domains, data analysts do not necessarily have sufficient knowledge about different data tables and application domains. It makes them unable to systematically elicit a series of topically-related and meaningful queries for insight discovery in target domains. We develop a NLI with a step-wise query recommendation module to assist users in choosing appropriate next-step exploration actions. The system adopts a data-driven approach to suggest semantically relevant and context-aware queries for application domains of users' interest based on their query logs. Also, the system helps users organize query histories and results into a dashboard to communicate the discovered data insights. With a comparative user study, we show that our system can facilitate a more effective and systematic data analysis process than a baseline without the recommendation module.Comment: 14 pages, 6 figure

Leveraging Historical Medical Records as a Proxy via Multimodal Modeling and Visualization to Enrich Medical Diagnostic Learning

Simulation-based Medical Education (SBME) has been developed as a cost-effective means of enhancing the diagnostic skills of novice physicians and interns, thereby mitigating the need for resource-intensive mentor-apprentice training. However, feedback provided in most SBME is often directed towards improving the operational proficiency of learners, rather than providing summative medical diagnoses that result from experience and time. Additionally, the multimodal nature of medical data during diagnosis poses significant challenges for interns and novice physicians, including the tendency to overlook or over-rely on data from certain modalities, and difficulties in comprehending potential associations between modalities. To address these challenges, we present DiagnosisAssistant, a visual analytics system that leverages historical medical records as a proxy for multimodal modeling and visualization to enhance the learning experience of interns and novice physicians. The system employs elaborately designed visualizations to explore different modality data, offer diagnostic interpretive hints based on the constructed model, and enable comparative analyses of specific patients. Our approach is validated through two case studies and expert interviews, demonstrating its effectiveness in enhancing medical training.Comment: Accepted by IEEE VIS 202

THE PROTON SPIN PUZZLE AND DEPOLARIZATION IN pˉp→ΛˉΛ\bar{p}p\to\bar{\Lambda}\Lambda

We point out that the measurement of target spin depolarization $D_{nn}$ in the $\bar{p}p\to\bar{\Lambda}\Lambda$ reaction may test dynamical mechanisms invoked to explain the proton spin puzzle revealed by polarized deep--inelastic scattering experiments. In particular, models with {\it negatively} polarized $\bar{s}s$ pairs in the proton wave function predict $D_{nn}<0$, whereas models with {\it positively} polarized gluons would predict $D_{nn}>0$.Comment: LaTeX file, 4 figures appended as uuencoded, compressed PostScript fil

Gauge bosons at zero and finite temperature

Gauge theories of the Yang-Mills type are the single most important building block of the standard model and beyond. Since Yang-Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Beyond perturbation theory, gauge-fixing in non-Abelian gauge theories is obstructed by the Gribov-Singer ambiguity. The construction and implementation of a method-independent gauge-fixing prescription to resolve this ambiguity is the most important step to describe gauge bosons beyond perturbation theory. Proposals for such a procedure, generalizing the perturbative Landau gauge, are described here. Their implementation are discussed for two example methods, lattice gauge theory and the quantum equations of motion. The most direct access to the properties of the gauge bosons is provided by their correlation functions. The corresponding two- and three-point correlation functions are presented at all energy scales. These give access to the properties of the gauge bosons, like their absence from the asymptotic physical state space, the absence of an on-shell mass pole, particle-like properties at high energies, and their running couplings. Furthermore, auxiliary degrees of freedom are introduced during gauge-fixing, and their properties are discussed as well. These results are presented for two, three, and four dimensions, and for various gauge algebras. Finally, the modifications of the properties of gauge bosons at finite temperature are presented. Evidence is provided that these reflect the phase structure of Yang-Mills theory. However, it is found that the phase transition is not deconfining the gauge bosons, although the bulk thermodynamical behavior is of a Stefan-Boltzmann type. The resolution of this apparent contradiction is also presented. This resolution also provides an explicit and constructive solution to the Linde problem.Comment: v2: 153 pages, 45 figures, revised, updated, and extended version submitted on invitation to Physics Reports; v3: Intermediate update, 152 pages, 45 figures, minor errors corrected, reference list extended; v3 minor typographical changes and corrections, added references, version to appear in Physics Report

Intravenous alteplase for stroke with unknown time of onset guided by advanced imaging: systematic review and meta-analysis of individual patient data

Background: Patients who have had a stroke with unknown time of onset have been previously excluded from thrombolysis. We aimed to establish whether intravenous alteplase is safe and effective in such patients when salvageable tissue has been identified with imaging biomarkers. Methods: We did a systematic review and meta-analysis of individual patient data for trials published before Sept 21, 2020. Randomised trials of intravenous alteplase versus standard of care or placebo in adults with stroke with unknown time of onset with perfusion-diffusion MRI, perfusion CT, or MRI with diffusion weighted imaging-fluid attenuated inversion recovery (DWI-FLAIR) mismatch were eligible. The primary outcome was favourable functional outcome (score of 0–1 on the modified Rankin Scale [mRS]) at 90 days indicating no disability using an unconditional mixed-effect logistic-regression model fitted to estimate the treatment effect. Secondary outcomes were mRS shift towards a better functional outcome and independent outcome (mRS 0–2) at 90 days. Safety outcomes included death, severe disability or death (mRS score 4–6), and symptomatic intracranial haemorrhage. This study is registered with PROSPERO, CRD42020166903. Findings: Of 249 identified abstracts, four trials met our eligibility criteria for inclusion: WAKE-UP, EXTEND, THAWS, and ECASS-4. The four trials provided individual patient data for 843 individuals, of whom 429 (51%) were assigned to alteplase and 414 (49%) to placebo or standard care. A favourable outcome occurred in 199 (47%) of 420 patients with alteplase and in 160 (39%) of 409 patients among controls (adjusted odds ratio [OR] 1·49 [95% CI 1·10–2·03]; p=0·011), with low heterogeneity across studies (I2=27%). Alteplase was associated with a significant shift towards better functional outcome (adjusted common OR 1·38 [95% CI 1·05–1·80]; p=0·019), and a higher odds of independent outcome (adjusted OR 1·50 [1·06–2·12]; p=0·022). In the alteplase group, 90 (21%) patients were severely disabled or died (mRS score 4–6), compared with 102 (25%) patients in the control group (adjusted OR 0·76 [0·52–1·11]; p=0·15). 27 (6%) patients died in the alteplase group and 14 (3%) patients died among controls (adjusted OR 2·06 [1·03–4·09]; p=0·040). The prevalence of symptomatic intracranial haemorrhage was higher in the alteplase group than among controls (11 [3%] vs two [&lt;1%], adjusted OR 5·58 [1·22–25·50]; p=0·024). Interpretation: In patients who have had a stroke with unknown time of onset with a DWI-FLAIR or perfusion mismatch, intravenous alteplase resulted in better functional outcome at 90 days than placebo or standard care. A net benefit was observed for all functional outcomes despite an increased risk of symptomatic intracranial haemorrhage. Although there were more deaths with alteplase than placebo, there were fewer cases of severe disability or death. Funding: None