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Objectives We have previously shown that pituitary cysts may affect growth hormone secretion. This study sought to determine cyst evolution during growth hormone treatment in children. Methods Forty-nine patients with short stature, a pituitary cyst, and at least two brain MRI scans were included. The percent of the pituitary gland occupied by the cyst (POGO) was calculated, and a cyst with a POGO of ≤15% was considered small, while a POGO >15% was considered large. Results Thirty-five cysts were small, and 14 were large. Five of the 35 small cysts grew into large cysts, while 6 of the 14 large cysts shrunk into small cysts. Of 4 cysts that fluctuated between large and small, 3 presented as large and 1 as small. Small cysts experienced greater change in cyst volume (CV) (mean=61.5%) than large cysts (mean=−0.4%). However, large cysts had a greater net change in CV (mean=44.2 mm3) than small cysts (mean=21.0 mm3). Older patients had significantly larger mean pituitary volume than younger patients (435.4 mm3 vs. 317.9 mm3) and significantly larger mean CV than younger patients (77.4 mm3 vs. 45.2 mm3), but there was no significant difference in POGO between groups. Conclusions Pituitary cyst size can vary greatly over time. Determination of POGO over time is a useful marker for determining the possibility of a pathologic effect on pituitary function since it factors both cyst and gland volume. Large cysts should be monitored closely, given their extreme, erratic behavior.

Background MRIs of the brain in patients with short stature have shown a number of abnormalities. Some of these radiological findings can have clinical significance. Here we have looked at MRI results in such a population. Objective To review the value and significance of the prevalence of all abnormal MRI findings of children with short stature who are to undergo growth hormone therapy (GHT). Materials and methods This study involved a retrospective review of MRI findings in all children prescribed GHT within a pediatric health network's database from Jan 2020 to Aug 2021. Post-gadolinium contrast enhanced brain and pituitary MRIs utilizing 2 mm slices were used to calculate pituitary volume. Pituitary volume was calculated using the ellipsoid formula (LxWxH/2). Pediatric patients diagnosed with non-acquired GHD or ISS, with MRIs having been performed between Jan 2020 and Aug 2021 and having been prescribed GHT by Aug 2021 were included in this study. Patients who experienced other endocrine abnormalities such as SGA, Turner Syndrome, and Noonan Syndrome were excluded. Patients with obstruction of sellar and parasellar religion due to movement artifacts or magnetic interference on their MRIs were also excluded. Results Of one hundred and twelve patients found, eighty one met criteria for inclusion in this study. Of the eighty one MRIs reviewed, twenty eight children, 34.6%, had normal pituitary anatomy and fifty three, 65.4%, had a pituitary abnormality. Out of the fifty three with a pituitary abnormality, forty three subjects, 81.1%, were determined to have a small pituitary volume, including significant pituitary hypoplasia. Ten subjects (18.9%) had an enlarged pituitary volume (pituitary hyperplasia). Of these ten patients who had an enlarged pituitary volume, eight were pubertal (80%). Nine children with a pituitary abnormality (16.9%) had additional structural anomalies on their MRIs. One had a small left frontal developmental venous anomaly. Two had Rathke's cleft cysts. Two had pars intermedia cysts. One had a small right parietal developmental venous anomaly. One had a small left parietal developmental venous anomaly. One had a left cerebellar tonsillar ectopia bordering on chiari malformation (.5 mm away on the coronal plane). One had a small lobulation (semi-bulbous projection) of the anterior pituitary gland, superior and anterior to the infundibular stalk. Conclusion Prevalence of brain abnormalities in children with short stature who are to undergo GHT is significant and warrants MRI evaluations in these subjects. Presentation: Saturday, June 11, 2022 1:00 p.m. - 3:00 p.m., Monday, June 13, 2022 12:58 p.m. - 1:03 p.m.

Background Pituitary cysts (PCs) may be related to the development of diminished growth hormone secretion because they may limit the proliferation of somatotrophs. This study seeks to investigate the mass effect of PCs on the pituitary function. Methods Patients aged 6-18 with cysts and follow-ups between 2007–21 were compared to normal controls (NCs) aged 6-18 from a neuroradiology center. Pituitary volume (PV) is the volume of the pituitary gland including the cyst, while net pituitary volume (netPV) is the volume of the pituitary gland excluding the cyst. Since NCs did not have PCs, only PV was utilized. PVs and netPVs are reported in mm3. Data were stratified into prepubertal (age < 11 yrs) and pubertal (age > 11 yrs). The Kruskal-Wallis One Way ANOVA on Ranks was utilized to compare multiple means, and the Kruskal-Wallis Multiple-Comparison Z Value test (with Bonferroni adjustment) was utilized for pairwise comparisons. Results The mean and median PVs of prepubertal GHD (n=37), ISS (n=5), and NCs (n=58) were 290.2 ± 109.7 and 305.0, 314.4 ± 100.8 and 299.8, and 246.8 ± 63.7 and 241.6, respectively. The difference between mean PVs of prepubertal GHD, ISS, and NCs was not significant. The mean and median PVs of pubertal GHD (n=58), ISS (n=33), and NCs (n=112) were 391.5 ± 163.5 and 370.2, 409.2 ± 215.8 and 382.9, and 424.2 ± 138.9 and 402.7, respectively. The difference between mean PVs of pubertal GHD, ISS, and NCs was not significant. For netPV, the mean and median values for prepubertal GHD and ISS patients were 252.2 ± 83.3 and 272.2, and 245.2 ± 85.7 and 244.9, respectively. The difference between mean netPVs of prepubertal GHD, ISS, and NCs was not significant. For netPV, the mean and median values for pubertal GHD and ISS patients were 332.7 ± 121.3 and 346.4, and 333.9 ± 146.1 and 330.7, respectively. The mean netPVs of pubertal GHD and ISS patients were both significantly lower than the mean PV of pubertal NCs. The mean and median PVs for cyst patients were 364.8 ± 170.0 and 347.8 which was not significantly different from the NCs. The mean and median netPVs for cyst patients were 307.3 ± 122.9 and 289.0 which was significantly different from the NCs (p Conclusion When considering the functional component of the pituitary gland, cyst volume should be subtracted from the overall pituitary gland. Presentation: Sunday, June 12, 2022 12:36 p.m. - 12:41 p.m., Monday, June 13, 2022 12:30 p.m. - 2:30 p.m.

Background Pituitary cysts may be implicated in short stature and affect growth hormone secretion. The natural history of cysts is not known in patients with GHD and ISS. Objective To characterize the progression of cyst volume (CV) and percentage of the gland occupied by the cyst (POGO) over time in GHD and ISS patients. Subjects and Methods A pediatric health system's database was queried for patients diagnosed with short stature and a cyst with at least one follow up MRI between 2007-21. Data up to 7 years after first follow up was included in this study. The mean and median follow up time were 1.32±1.24 and 1.00. Cysts with a POGO≤15% were considered small, while a POGO>15% were considered large. Results The mean and median %ΔCV for all patients for all their follow up MRIs were 38.27%±179.14 and 0%. The mean and median %ΔPOGO for all patients were 38.32%±219.85 and -5.79%. The mean and median %ΔCV for patients with a small cyst (SC) (n=34) were 61.49%±215.60 and 0%. The mean and median %ΔPOGO for patients with a SC were 61.62%±267.25 and -2.89%. The mean and median %ΔCV for patients with a large cyst(LC)(n=14) were -0.4% ±-79.25 and 0%. The mean and median %ΔPOGO for patients with a LC were -1.08%±90.50 and -15.67%. 5 of the 35(14.3%) SCs grew into LCs and stayed large while 6 of the 14 LCs shrunk into SCs. 4 cysts fluctuated between large and small: 3 started large and 1 started small. CV of patients with LCs has a significant negative correlation with time (-0.37, p=0.01). The slope of the regression line is -0.01 mm3/month. The CV of patients with SCs does not show any change in time (-0.02, p=0.84). There is no significant difference in POGO (p=0.86) or in CV (p=0.96) in GHD and ISS patients. In GHD and ISS patients, the difference in POGO is different in each group at each MRI date (p=0.02), but not in CV (p=0.38). GHD patients had an average ΔPOGO of -1.05, while ISS patients had an average ΔPOGO of 1.26. Conclusion POGO can change greatly over time. LCs tend to take up less of the gland over time. SCs tend not to change significantly over time, but a minority can still enlarge and need to be monitored. So far, there have been no significant clinical consequences related to these cysts. Presentation: Monday, June 13, 2022 12:30 p.m. - 2:30 p.m.

We have shown that short children have significantly reduced pituitary volume (PV)s and have speculated PV as a cause for diminished chronic growth hormone (GH) secretion and poor growth. In this study, we further elucidate the role of PV in the etiology of short stature (SS) in a larger cohort of siblings (SBs).The database of a Peds Endo Center between 2013-21 was queried for siblings with SS who underwent a GH Stimulation test (GHST) and MRI evaluation. Their results were compared with normal controls (NCs) as previously reported. 129 SBs of 60 families were compared to 170 NCs. SBs were divided into 3 groups (GPs). GP1 (n=79) consisted of families with only GHD. GP2 (n=12) contained families with only ISS SBs. GP3 (n=38) comprised families with mixed GHD and ISS. SBs 11 yrs were considered prepubertal (prePB) and pubertal (PB), RSP. The mean (MN) and median (MD) age for both prePB and PB SBs were significantly different (p 0.05). The 32 PB patients in GP3 had a mean PV of 316.17± 197.53 mm3, which was significantly different from that of the PB NCs of 424.6 ± 138.4 mm3 (p Presentation: Saturday, June 11, 2022 1:00 p.m. - 3:00 p.m.

Background Patients with diminished growth hormone (GH) secretion are candidates for GH therapy (GHT). The GH stimulation test (GHST) is considered the gold standard for the diagnosis of GH deficiency (GHD), yet its efficacy has been questioned. In this study we explore the GHST and PV's ability to define GHD and determine their individual ability to predict GHT outcomes. Subjects and Methods A database at a Pediatric Endocrinology center was queried for patients aged 6-18 yrs who underwent a GHST, MRI, and GHT between 1/2018 - 1/2021. Patients with a first follow up (FU) between 3 and 9 months were included; of these patients, second FUs were included if they occurred between 9 and 15 months. Patients with relevant comorbidities, those with GHST peak ≥ 10.0 ng/mL, and nonadherent patients were excluded. MRIs were acquired on a Philips 1.5 or 3.0 T scanner (2mm slices) and PV was calculated using the ellipsoid formula (LxWxH/2). PV and height were converted to SDS. Response to treatment was defined as change in height SDS over the assessed time interval. A multiple linear regression was utilized to analyze the response to GHT relative to peak GH and PV, with initial height and age at stimulation included as covariates. The relationship between peak GH and PV SDS was analyzed with a Pearson correlation Results The first FU ranged between 3.1 and 8.9 months, and the second FU ranged between 9.0 and 14.9 months. 145 patients had one FU, and 83 patients had two FUs. Peak GH and PV SDS were not correlated (r=0.03). Patients who were relatively shorter for their age and gender at stimulation had higher growth rates in the first interval, but not in the second interval. Both PV and peak GH provided information about response to GHT. PV SDS negatively predicted the relative growth response to treatment in the first interval (slope=-0.03, p=0.048). However, PV only explained 3.7% of variation in growth. PV SDS was not a useful predictor of response in the second interval (slope=-0.01, p=0.693). Peak GH was a predictor of response to GHT in the first interval only after accounting for age at stimulation and initial height (slope=-0.01, p=0.032; r2=0.01). Peak GH was a predictor of response in the second interval (slope=-0.02, p=0.040), explaining 5.1% of the variation in growth. Conclusion Since peak GH and PV were not correlated, they likely reflect different physiological processes. PV and peak GH both provide information about response to GHT, so they should both be utilized to determine eligibility for GHT. Presentation: Saturday, June 11, 2022 1:00 p.m. - 3:00 p.m.

This study aims to elucidate the impact of frailty on spontaneous intracranial hemorrhage (SICH) patient outcomes in the United States.This is a single center retrospective chart review of all adult patients (≥18 years old) admitted with a primary diagnosis of SICH due to hypertension, amyloid angiopathy, and coagulopathy from 2014-2017. The studied variables included length of stay, age, sex, ICH score variables, medications, and frailty as measured by the modified Frailty Index (mFI).A total of 240 patients with 248 SICH were included in the analysis. In this study, mFI was not predictive of overall mortality (p = 0.12). To further investigate this issue, patients with ICH scores of 2 or 3 were separately analyzed to assess the impact of mFI on moderate ICH cases. However, mFI was also not associated with increased hospital mortality in moderate ICH cases (p = 0.812). In bivariate Spearman analysis, mFI significantly correlated with several outcome measures including modified Rankin Scale (MRS) at discharge (p = 0.01), but ICH score also correlated with these outcomes (p 0.001). Although ICHmFI scores were both predictive of MRS with linear regression, multivariate demonstrated that the ICH score was the only independent risk factor for MRS (p = 0.698, p 0.001 respectively).Frailty, as measured by the mFI, was not an independent risk factor for increased mortality or worse outcomes in SICH patients. This study does not support incorporating the mFI score for SICH patients for prognostication.

This paper presents a wireless transceiver intended for insect-based wireless sensor networks (WSNs). The transceiver utilizes several design techniques developed to meet the challenging low power and low size requirements in insect-based WSNs. The techniques include current reuse in the voltage-controlled oscillator (VCO) and power amplifier (PA), fast PLL on/off switching for low-power on/off keying (OOK) modulation, and switching between transmit and receive (TX/RX) modes without an off-chip switch. Also, the VCO, PA, low noise amplifier (LNA), OOK modulator, and TX/RX switch are co-designed and integrated into a single block to reduce the system complexity significantly. The transceiver is designed and fabricated in a 0.13-μm CMOS process. The transmitter provides an output power in the range of -30 dBm to -4.4 dBm while consuming an average power of 1.2 mW to 4.5 mW. The phase locked-loop (PLL) does not use a high-Q external resonator, and its phase noise depends on the PA output power because of the current reuse in the VCO and PA. The PLL phase noise at 1 MHz offset at 2.4 GHz varies from -103.3 dBc/Hz to -116.7 dBc/Hz. The receiver achieves a sensitivity of -90 dBm at 1 Mbps data rate for a BER = 0.1%. An example wireless sensor node design utilizing the proposed wireless transceiver achieves a modest weight of 1 gram, and a small form factor of 12.5 mm × 12.5 mm.

Many insect families have evolved to produce and detect complex singing patterns for the purposes of mating, display of dominance, predator escape, and other needs. While the mechanisms of sound production by insects have been thoroughly studied, man-machine exploitation of such mechanisms has remained unreported. We therefore describe a method to modulate the frequency spectrum in the chirp call of a singing insect, Gampsocleis gratiosa (Orthoptera: Tettigoniidae), a large katydid indigenous to China and commonly known as Guo Guo or Chinese Bush Cricket. The chirp modulation was achieved through the contact of a ribbon of Ionic Polymer-Metal Composite (IPMC) against wing of the insect. The IPMC effectively served as an actuator when a small DC voltage was applied to the ribbon’s faces. By applying a sequential on/off voltage waveform to the IPMC ribbon, the katydid’s chirp was modulated in a corresponding manner. This configuration can be used as part of a broader application of using singing insects to harness their acoustic power to produce and propagate machine-induced messages into the acoustic environment.

Topical corticosteroids are the cornerstone of treatment for the majority of psoriasis patients. However, potential side effects of topical corticosteroids (i.e., cutaneous atrophy, telangiectasias, hypothalamic-pituitary axis suppression), coupled with the complex pathophysiology of psoriasis and the individual needs/preferences of psoriasis patients, represent a few of the limitations associated with topical corticosteroid monotherapy. While the combination of some agents with varying mechanisms of action has proven to be an effective strategy for improving efficacy and reducing concomitant drug application, others have displayed less efficacy, harm, and/or reduced cost-effectiveness. The purpose of this article is to review novel topical therapeutic combinations for the management of psoriasis and explore the role compounding pharmacies can have in providing healthcare providers and patients with effective and affordable alternative psoriasis therapies.

Purpose We developed and evaluated a training procedure for marking the endpoints of the ellipsoid zone (EZ), also known as the inner segment/outer segment (IS/OS) border, on frequency domain optical coherence tomography (fdOCT) scans from patients with retinitis pigmentosa (RP). Methods A manual for marking EZ endpoints was developed and used to train 2 inexperienced graders. After training, an experienced grader and the 2 trained graders marked the endpoints on fdOCT horizontal line scans through the macula from 45 patients with RP. They marked the endpoints on these same scans again 1 month later. Results Intragrader agreement was excellent. The intraclass correlation coefficient (ICC) was 0.99, the average difference of endpoint locations (19.6 μm) was close to 0 μm, and the 95% limits were between -284 and 323 μm, approximately ±1.1°. Intergrader agreement also was excellent. The ICC values were 0.98 (time 1) and 0.97 (time 2), the average difference among graders was close to zero, and the 95% limits of these differences was less than 350 μm, approximately 1.2°, for both test times. Conclusions While automated algorithms are becoming increasingly accurate, EZ endpoints still have to be verified manually and corrected when necessary. With training, the inter- and intragrader agreement of manually marked endpoints is excellent. Translational relevance For clinical studies, the EZ endpoints can be marked by hand if a training procedure, including a manual, is used. The endpoint confidence intervals, well under ±2.0°, are considerably smaller than the 6° spacing for the typically used static visual field.

Due to ongoing improvements in the performance and programmability of commercially available Graphics Processor Units (GPUs), substantial increases in the execution speed of EM propagation analysis through ray tracing is now attainable. This paper presents recent results where RF ray tracing has been applied to analyze signal propagation over complex urban 3D scene models. The ray trace algorithms were programmed to operate as parallel processes over hundreds of core processors that make up the architecture of off-the-shelf GPU chips.

A clear and accurate understanding of communication network performance is essential, especially where all layers of the protocol stack - from physical propagation to application transport protocols - must be accounted for. While some solutions exist for RF communications over `open-terrain' areas, the urban environment is particularly challenging. To meet this challenge, a server-based, real-time solution for assessing complex communication and network effects in urban environments has been developed. By combining advanced RF ray-tracing propagation modeling and a full network simulator, the Scalable Urban Network Simulation (SUNS) software is able to provide accurate communications effects services. SUNS supports tactical modeling and simulation by predicting electro-magnetic signal coverage and path loss through application of a full 3D physical knowledge of the urban environment and terrain features. The commercial OPNET network simulator is used as the core of the system, with SUNS operations supported through a custom OPNET model that functions as a modeling and simulation server. The server, in turn, communicates with other node models within the OPNET simulation. In the approach, urban propagation data are pre-computed using high-performance computing (HPC) resources utilizing ray traced models of the urban scene.

To improve our understanding of glaucomatous damage as seen on circumpapillary disc scans obtained with frequency-domain optical coherence tomography (fdOCT), fdOCT scans were compared to images of the peripapillary retinal nerve fiber (RNF) bundles obtained with an adaptive optics-scanning light ophthalmoscope (AO-SLO).The AO-SLO images and fdOCT scans were obtained on 6 eyes of 6 patients with deep arcuate defects (5 points ≤-15 db) on 10-2 visual fields. The AO-SLO images were montaged and aligned with the fdOCT images to compare the RNF bundles seen with AO-SLO to the RNF layer thickness measured with fdOCT.All 6 eyes had an abnormally thin (1% confidence limit) RNF layer (RNFL) on fdOCT and abnormal (hyporeflective) regions of RNF bundles on AO-SLO in corresponding regions. However, regions of abnormal, but equal, RNFL thickness on fdOCT scans varied in appearance on AO-SLO images. These regions could be largely devoid of RNF bundles (5 eyes), have abnormal-appearing bundles of lower contrast (6 eyes), or have isolated areas with a few relatively normal-appearing bundles (2 eyes). There also were local variations in reflectivity of the fdOCT RNFL that corresponded to the variations in AO-SLO RNF bundle appearance.Relatively similar 10-2 defects with similar fdOCT RNFL thickness profiles can have very different degrees of RNF bundle damage as seen on fdOCT and AO-SLO.While the results point to limitations of fdOCT RNFL thickness as typically analyzed, they also illustrate the potential for improving fdOCT by attending to variations in local intensity.

Background Kallikrein 6 (KLK6) is a newly identified member of the kallikrein family of secreted serine proteases that prior studies indicate is elevated at sites of central nervous system (CNS) inflammation and which shows regulated expression with T cell activation. Notably, KLK6 is also elevated in the serum of multiple sclerosis (MS) patients however its potential roles in immune function are unknown. Herein we specifically examine whether KLK6 alters immune cell survival and the possible mechanism by which this may occur. Methodology/Principal Findings Using murine whole splenocyte preparations and the human Jurkat T cell line we demonstrate that KLK6 robustly supports cell survival across a range of cell death paradigms. Recombinant KLK6 was shown to significantly reduce cell death under resting conditions and in response to camptothecin, dexamethasone, staurosporine and Fas-ligand. Moreover, KLK6-over expression in Jurkat T cells was shown to generate parallel pro-survival effects. In mixed splenocyte populations the vigorous immune cell survival promoting effects of KLK6 were shown to include both T and B lymphocytes, to occur with as little as 5 minutes of treatment, and to involve up regulation of the pro-survival protein B-cell lymphoma-extra large (Bcl-XL), and inhibition of the pro-apoptotic protein Bcl-2-interacting mediator of cell death (Bim). The ability of KLK6 to promote survival of splenic T cells was also shown to be absent in cell preparations derived from PAR1 deficient mice. Conclusion/Significance KLK6 promotes lymphocyte survival by a mechanism that depends in part on activation of PAR1. These findings point to a novel molecular mechanism regulating lymphocyte survival that is likely to have relevance to a range of immunological responses that depend on apoptosis for immune clearance and maintenance of homeostasis.

A well known preventive replacement policy is the block replacement policy (BRP). In such a policy the item undergoes a planned replacement at a sequence of equally spaced time points independent of failure history. The main advantage of a BRP is its simplicity, because under this policy it is unnecessary to keep detailed records about times of failures or ages of items. The main drawback of a BRP is that at planned replacement times we may be replacing practically new items. In this paper we study a modified BRP which is free of this drawback. We calculate the expected cost of following a modified BRP for lifetime distributions possessing a special structure and illustrate it for the case of an Erlang distribution. A numerical comparison is made between a modified BRP and a standard BRP for the special case of a two stage Erlang distribution.

The model for a modified block replacement policy (MBRP) is extended to include running costs. An illustrative example is worked out for the case when item life is exponentially distributed and marginal running cost per unit time increases linearly with the age of the item.

Linear asymptotically unbiased estimators of ξ quantiles, x ξ 0 < ξ < 1, of location-scale distributions are considered. These are based on two or three order statistics suitably selected in a neighborhood of the sample quantile X (N), N = [nξ] + 1, where n is the sample size. The estimators are easy to calculate and are substantially more efficient than the nonparametric estimator ξ = X (N). The estimators are tabulated for selected values of ξ for the normal and extreme value (Gumbel) distributions. Also given are the asymptotic relative efficiencies of these estimators when compared with the maximum likelihood estimator of x ξ based on all n observations.

In this paper we study the flow of traffic on roads for which passing is not permitted. Such traffic conditions exist in rural areas, hilly or mountainous regions, tunnels, etc. The traffic flow process is considered as taking place in a one directional road of infinite length, with passing not permitted. This paper studies measures of traffic flow in a road where vehicles have one of two free speeds. Measures of traffic flow are obtained for general vehicle entrance processes and derived explicitly for the homogeneous Poisson case.

Two widely used preventive replacement policies are the age replacement policy (ARP) and the block replacement policy (BRP). Another replacement policy is the failure replacement policy (FRP) in which no preventive replacements are made at all. In this paper we give a rule for choosing the least costly of the above three policies under conditions specified in the paper. The implementation of this rule is illustrated for two special cases, where the distribution of item life times is uniform, or 2-stage Erlang.

”The Principal - Contract Administrator and Instructional Leader," published in the February 1980 Bulletin, motivated this writer to say that the advice outlined in that article would bring a principal “misery, disaster and utter chagrin." Presented here is the remainder of Ben Epstein's letter published last month in the Bulletin.

Almost all the analytical models in the literature for traffic flow on two-lane roads are concerned with steady state situations, assuming that passing is possible at any point along the road. In this paper we study the steady state situation, assuming that passing is possible only at passing points, which are located at equal distances along the road. The mathematical model, presented in this paper, shows how expected velocities, expected driver loss time and platoon length are affected by such characteristics as speeds of fast and slow vehicles, rates at which fast and show vehicles enter the road, spacing of passing opportunities, and probability of a vehicle being able to pass given a passing opportunity.

A number of writers have observed that the particle size distributions obtained from some breakage processes appear to be logarithmico-normal. There have been virtually no attempts to explain this phenomenon. In this paper a statistical model is constructed for a breakage mechanism which will generate size distributions which are asymptotically logarithmico-normal. In this model, Fn(x), the distribution function of the particle sizes, after n steps of the breakage process, is the distribution function of the product of (n + 1) independent random variables and hence, by the central limit theorem, is asymptotically logarithmico-normal.

This paper describes statistical methods for testing hypotheses about the mean of an exponential distribution of life. Advantage is taken of the time-ordered nature of life test data to shorten substantially the time required to reach a decision. Replacement, non-replacement, sequential, non-sequential, and truncated procedures are described. Some useful tables are given at the end of the paper.

In recent years there has been an increasing interest in the development of statistical theories of strength. A main aim of these theories is to explain in a reasonable way such things as the dependence of the strength of specimens on their volume or length. In this paper it is pointed out that the problems posed by these models are equivalent to an important problem in mathematical statistics, namely, the distribution of the smallest value in samples of size n drawn from a population having some probability density function f(x). The calculations made by mathematical statisticians give a far more complete description of the results to be expected than do the estimates to be found up to now in the technical literature.

The theory of extreme values finds many applications in modern technology. This paper is an attempt to unfold the basic elements of the theory. Frequent examples are given to illustrate both derivations and application.

Part I of this paper was published in the previous issue of Technometrics, (Vol. 2, No. 1, February 1960). In Part I Dr. Epstein describes several graphical and analytical procedures for testing the assumption that the underlying distribution of life is exponential. This portion of the paper contains numerical examples illustrative of these procedures.

In this paper it is shown that the statistical theory of the distribution of extreme values is pertinent to the study of the way in which the breakdown strengths of paper capacitors depend on capacitor size. The theory presented in this paper permits a quantitative explanation of this phenomenon and results are given which should be useful to design engineers.