Confidence Bands for Distribution Functions: A New Look at the Law of the Iterated Logarithm

We present a general law of the iterated logarithm for stochastic processes on the open unit interval having subexponential tails in a locally uniform fashion. It applies to standard Brownian bridge but also to suitably standardized empirical distribution functions. This leads to new goodness-of-fit tests and confidence bands which refine the procedures of Berk and Jones (1979) and Owen (1995). Roughly speaking, the high power and accuracy of the latter procedures in the tail regions of distributions are essentially preserved while gaining considerably in the central region

A law of the iterated logarithm for Grenander's estimator

In this note we prove the following law of the iterated logarithm for the Grenander estimator of a monotone decreasing density: If $f(t_0) > 0$, $f'(t_0) < 0$, and $f'$ is continuous in a neighborhood of $t_0$, then \begin{eqnarray*} \limsup_{n\rightarrow \infty} \left ( \frac{n}{2\log \log n} \right )^{1/3} ( \widehat{f}_n (t_0 ) - f(t_0) ) = \left| f(t_0) f'(t_0)/2 \right|^{1/3} 2M \end{eqnarray*} almost surely where $M \equiv \sup_{g \in {\cal G}} T_g = (3/4)^{1/3}$ and T_g \equiv \mbox{argmax}_u \{ g(u) - u^2 \} ; here ${\cal G}$ is the two-sided Strassen limit set on $R$. The proof relies on laws of the iterated logarithm for local empirical processes, Groeneboom's switching relation, and properties of Strassen's limit set analogous to distributional properties of Brownian motion.Comment: 11 pages, 3 figure

Marshall's lemma for convex density estimation

Marshall's [Nonparametric Techniques in Statistical Inference (1970) 174--176] lemma is an analytical result which implies $\sqrt{n}$--consistency of the distribution function corresponding to the Grenander [Skand. Aktuarietidskr. 39 (1956) 125--153] estimator of a non-decreasing probability density. The present paper derives analogous results for the setting of convex densities on $[0,\infty)$.Comment: Published at http://dx.doi.org/10.1214/074921707000000292 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

The density ratio of Poisson binomial versus Poisson distributions

Let $b(x)$ be the probability that a sum of independent Bernoulli random variables with parameters $p_1, p_2, p_3, \ldots \in [0,1)$ equals $x$, where $\lambda := p_1 + p_2 + p_3 + \cdots$ is finite. We prove two inequalities for the maximal ratio $b(x)/\pi_\lambda(x)$, where $\pi_\lambda$ is the weight function of the Poisson distribution with parameter $\lambda$

Top-down and bottom-up modulation of language related areas – An fMRI Study

BACKGROUND: One major problem for cognitive neuroscience is to describe the interaction between stimulus and task driven neural modulation. We used fMRI to investigate this interaction in the human brain. Ten male subjects performed a passive listening and a semantic categorization task in a factorial design. In both tasks, words were presented auditorily at three different rates. RESULTS: We found: (i) as word presentation rate increased hemodynamic responses increased bilaterally in the superior temporal gyrus including Heschl's gyrus (HG), the planum temporale (PT), and the planum polare (PP); (ii) compared to passive listening, semantic categorization produced increased bilateral activations in the ventral inferior frontal gyrus (IFG) and middle frontal gyrus (MFG); (iii) hemodynamic responses in the left dorsal IFG increased linearly with increasing word presentation rate only during the semantic categorization task; (iv) in the semantic task hemodynamic responses decreased bilaterally in the insula with increasing word presentation rates; and (v) in parts of the HG the hemodynamic response increased with increasing word presentation rates during passive listening more strongly. CONCLUSION: The observed "rate effect" in primary and secondary auditory cortex is in accord with previous findings and suggests that these areas are driven by low-level stimulus attributes. The bilateral effect of semantic categorization is also in accord with previous studies and emphasizes the role of these areas in semantic operations. The interaction between semantic categorization and word presentation in the left IFG indicates that this area has linguistic functions not present in the right IFG. Finally, we speculate that the interaction between semantic categorization and word presentation rates in HG and the insula might reflect an inhibition of the transfer of unnecessary information from the temporal to frontal regions of the brain

Combination of endobronchial bronchoscopic debulking and bronchoplastic segmentectomy of an obstructive neuroendocrine tumour: probably the least invasive approach.

We report the case of a female patient with an obstructing well-differentiated neuroendocrine tumour in the apical segment of the completely atelectatic right lower lobe. Bronchoscopic debulking of the tumour lead to re-ventilation of the remaining lobe, allowing to perform a lung-sparing bronchoplastic resection of the affected segment by uniportal video-assisted thoracic surgery

Case report: Post-thoracic surgery acquired venous thoracic outlet syndrome

Thoracic outlet syndrome (TOS) is a rare entity responsible for the vascular and/or nervous symptoms of the upper limbs. Unlike the congenital anatomical anomalies that cause TOS, acquired etiologies are even less common. Here, we report the case of a 41-year-old male with iatrogenic acquired TOS secondary to complex chest wall surgery for chondrosarcoma of the manubrium sterni; he was diagnosed with chondrosarcoma of the manubrium sterni in November, 2021. After staging was completed, primary surgery was performed. The operation was complex, with en-bloc resection of the manubrium sterni; the upper part of the corpus sterni; the first, second, and third bilateral parasternal ribs; and the medial clavicles, whose stumps were fixed on the first ribs. We reconstructed the defect using a double Prolene mesh, and bridged the second and third ribs on each side using two screwed plates. Finally, the wound was covered with pediculated musculocutaneous flaps. A few days after the operation, the patient presented with swelling in the left upper limb. Doppler ultrasound revealed slowing-down of the left subclavian vein flow, which was confirmed via thoracic computed tomography angiography. Systemic anticoagulation was initiated, and the patient began rehabilitation physiotherapy six weeks postoperatively. Symptoms had resolved by the 8-week outpatient follow-up, and anticoagulation therapy was stopped at three months; radiological follow-up demonstrated an improvement in subclavian vein flow without thrombosis. To the best of our knowledge, this is the first description of acquired venous TOS after thoracic surgery. Conservative treatment was found to sufficiently avoid the need for more invasive methods

Robotic vs. Transsternal Thymectomy: A Single Center Experience over 10 Years.

INTRODUCTION Thymomas are the most common tumors of the mediastinum. Traditionally, thymectomies have been performed through a transsternal (TS) approach. With the development of robot-assisted thoracic surgery (RATS), a promising, minimally invasive, alternative surgical technique for performing a thymectomy has been developed. In the current paper, the oncological and surgical outcomes of the TS vs. RATS thymectomies are discussed. METHODS For the RATS thymectomy, two 8 mm working ports and one 12 mm camera port were used. In the transsternal approach, we performed a median sternotomy and resected the thymic tissue completely, in some cases en bloc with part of the lung and/or, more frequently, a partial pericardiectomy with consequent reconstruction using a bovine pericardial patch. The decisions for using the TS vs. RATS methods were mainly based on the suspected tumor invasion of the surrounding structures on the preoperative CT scan and tumor size. RESULTS Between January 2010 and November 2020, 149 patients were submitted for an anterior mediastinal tumor resection at our institution. A total of 104 patients met the inclusion criteria. One procedure was performed through a hemi-clamshell incision. A total of 81 (78%) patients underwent RATS procedures, and 22 (21.1%) patients were treated using a transsternal (TS) tumor resection. Thymoma was diagnosed in 53 (51%) cases. In the RATS group, the median LOS was 3.2 ± 2.8 days and the median tumor size was 4.4 ± 2.37 cm compared to the TS group, which had a median LOS of 9 ± 7.3 days and a median tumor size of 10.4 ± 5.3 cm. Both differences were statistically significant (p < 0.001). Complete resection was achieved in all patients. CONCLUSION While larger and infiltrating tumors (i.e., thymic carcinomas) were usually resected via a sternotomy, the RATS procedure is a good alternative for the resection of thymomas of up to 9.5 cm, and the thymectomy is a strong approach for myasthenia gravis. The oncological outcomes and survival rates were not influenced by the chosen approach

A structured curriculum for the acquisition of basic surgical endoscopic skills for surgical residents and quantification of skills improvement.

INTRODUCTION New strategies and methods are needed to ensure that new generations can train and acquire surgical skills in a safe environment. MATERIALS AND METHODS From January 2020 to October 2020, we performed a single centre, prospective observational cohort study. 19 participants (15 students, 4 residents) enrolled and 16 participants (13 students, 3 residents) successfully completed the curriculum. We performed a quantitative data analysis to evaluate its effectiveness in gaining and improving basic surgical endoscopic skills. RESULTS The time for single knot tying pre-, mid-, and post-training was reduced significantly, the average time (sec) decreased by 79.5 % (p < 0.001), the total linear distance (cm) by 74.5 % (p < 0.001) and the total angular distance (rad) by 71.7 % (p < 0.001). The average acceleration (mm/s2) increased by 20 % (p = 0.041). Additionally, the average speed increased by 23.5 % (p < 0.001), while motion smoothness (m/s3) increased by 20.4 % (p = 0.02). CONCLUSION The obtained performance scores showed a significant increase in participants improving their basic surgical performance skills on the endoscopic simulator. This curriculum can be easily implemented in any surgical specialty as part of the residency training curriculum before first exposure in the operation room. All 16 participants recommended the implementation of such simulator training in their surgical training curriculum

The Adsorption of Per- and Polyfluoroalkyl Substances (PFASs) onto Ferrihydrite Is Governed by Surface Charge

An improved quantitative and qualitative understanding of the interaction of per- and polyfluoroalkyl substances (PFASs) and short-range ordered Fe (hydr)oxides is crucial for environmental risk assessment in environments low in natural organic matter. Here, we present data on the pH-dependent sorption behavior of 12 PFASs onto ferrihydrite. The nature of the binding mechanisms was investigated by sulfur K-edge X-ray absorption near-edge structure (XANES) spectroscopy and by phosphate competition experiments. Sulfur K-edge XANES spectroscopy showed that the sulfur atom of the head group of the sulfonated PFASs retained an oxidation state of +V after adsorption. Furthermore, the XANES spectra did not indicate any involvement of inner-sphere surface complexes in the sorption process. Adsorption was inversely related to pH (p &lt; 0.05) for all PFASs (i.e., C-3-C-5 and C-7-C-9 perfluorocarboxylates, C-4, C-6, and C-8 perfluorosulfonates, perfluorooctane sulfonamide, and 6:2 and 8:2 fluorotelomer sulfonates). This was attributed to the pH-dependent charge of the ferrihydrite surface, as reflected in the decrease of surface zeta-potential with increasing pH. The importance of surface charge for PFAS adsorption was further corroborated by the observation that the adsorption of PFASs decreased upon phosphate adsorption in a way that was consistent with the decrease in ferrihydrite zeta-potential. The results show that ferrihydrite can be an important sorbent for PFASs with six or more perfluorinated carbons in acid environments (pH &lt;= 5), particularly when phosphate and other competitors are present in relatively low concentrations