Maximal Denumerant of a Numerical Semigroup With Embedding Dimension Less Than Four

Given a numerical semigroup $S =$ and $s\in S$, we consider the factorization $s = c_1 a_1 + c_2 a_2 +... + c_t a_t$ where $c_i\ge0$. Such a factorization is {\em maximal} if $c_1+c_2+...+c_t$ is a maximum over all such factorizations of $s$. We show that the number of maximal factorizations, varying over the elements in $S$, is always bounded. Thus, we define \dx(S) to be the maximum number of maximal factorizations of elements in $S$. We study maximal factorizations in depth when $S$ has embedding dimension less than four, and establish formulas for \dx(S) in this case.Comment: Main results are unchanged, but proofs and exposition have been improved. Some details have been changed considerably including the titl

Novel detection schemes and automated image analysis algorithms for planar chromatography and gel electrophoresis

After a detailed introduction to Charge Coupled Devices (CCDs) and a discussion of personal computer capabilities, examples of their applications involving novel analytical techniques are presented;A new laser-based indirect fluorometric detection method for thin-layer chromatography is demonstrated with digitally controlled two-dimensional scanning and computer-aided image acquisition and vision. Utilizing this mode, universal detection is possible without derivatization, with a detection limit of 6 pg; 100 times lower than with human vision;A detection scheme for DNA in agarose slab gel electrophoresis based on ultraviolet absorption allows for convenient in situ monitoring of conventional gels via a CCD camera system, which greatly improves detectability compared to previous applications of this detection mode. With the use of the CCD system, low light level images can be acquired rapidly with minimal noise. Further on-line processing of the image allows one to correct for background and lighting variations and other non-random noise. The detection limit is about 5 ng of double-stranded DNA per band, which is at least 25 times lower than those obtained previously for UV absorption;The UV imaging method, along with a native fluorescence scheme, is demonstrated for detection of proteins in agarose slab gels. Detectability is comparable to traditional visualization schemes based on coomassie blue staining;A computerized method for correcting systematic signal distortions of images from slab gel electrophoresis is presented. The method is useful for interpretation of one-dimensional slab gel electrophoresis images where the information is manifested in rectangular shaped bands and the distortions can be described by low order polynomial functions. The purpose is to eliminate human judgement and interaction from the process, which is necessary for automated analysis of electrophoretic gels;A computerized expert system is introduced for the reduction of data acquisition in random access two-dimensional scanners or imaging devices where multiple scans are necessary to identify all features. The various areas of the image are probed to different extents based on the accumulated signal to noise ratio (SNR) of each area, resulting in a constant SNR throughout the final image. The method is applied to sequencing gel interpretation

Goto Numbers of a Numerical Semigroup Ring and the Gorensteiness of Associated Graded Rings

The Goto number of a parameter ideal Q in a Noetherian local ring (R,m) is the largest integer q such that Q : m^q is integral over Q. The Goto numbers of the monomial parameter ideals of R = k[[x^{a_1}, x^{a_2},..., x_{a_{\nu}}]] are characterized using the semigroup of R. This helps in computing them for classes of numerical semigroup rings, as well as on a case-by-case basis. The minimal Goto number of R and its connection to other invariants is explored. Necessary and sufficient conditions for the associated graded rings of R and R/x^{a_1}R to be Gorenstein are also given, again using the semigroup of R.Comment: 36 pages, corrected typos and improved exposition throughout. To appear in Communications in Algebr

A Comparative Analysis Of Army Body Composition Standards For Women

International Journal of Exercise Science 13(7): 1275-1282, 2020. The aim of this study was to compare body fat percentage (BF%) of women measured using the U.S. Army standard body composition assessment (ABC) and two common laboratory measures of body composition to evaluate the efficacy of ABC within this population. The BF% of 27 women (21.5 ± 1.8 years) was assessed using the 7-site skinfold, air plethysmography, and ABC measurements. The initial physical fitness test (IPFT) was used to determine if participants met the criteria required for admittance into basic combat training. A repeated measures ANOVA identified differences in BF% between the three assessment methods, (F (2, 52) = 22.83, p \u3c .001, η2p = .47). Pairwise comparisons revealed that mean BF% obtained using the ABC (29.3 ± 7.7 %) was significantly higher (p = .042) than BF% measured using air plethysmography (26.9 ± 8.4 %). ABC and air plethysmography measured BF% was significantly higher (both p \u3c .001) than BF% obtained from skinfold assessment (22.2 ± 5.9 %). Of the 27 total participants, 4 (14.8%) passed IPFT but failed to meet the Army body composition standards using the ABC method. The primary findings of this study suggest that the overestimation of BF% by the ABC method could lead to an unnecessary delay in enlistment for women approaching the upper threshold of the Army’s acceptable body composition standards. Alternative methods of assessing body composition in this population should be explored. However, skinfold assessment does not appear to be a suitable alternative to the ABC

The Maximal Denumerant of a Numerical Semigroup

Given a numerical semigroup S = and n in S, we consider the factorization n = c_0 a_0 + c_1 a_1 + ... + c_t a_t where c_i >= 0. Such a factorization is maximal if c_0 + c_1 + ... + c_t is a maximum over all such factorizations of n. We provide an algorithm for computing the maximum number of maximal factorizations possible for an element in S, which is called the maximal denumerant of S. We also consider various cases that have connections to the Cohen-Macualay and Gorenstein properties of associated graded rings for which this algorithm simplifies.Comment: 13 Page

Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science

Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in data science. The group consisted of 25 undergraduate faculty from a variety of institutions in the United States, primarily from the disciplines of mathematics, statistics, and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in data science

Pathogenic MAST3 Variants in the STK Domain Are Associated with Epilepsy

Objective: The MAST family of microtubule-associated serine–threonine kinases (STKs) have distinct expression patterns in the developing and mature human and mouse brain. To date, only MAST1 has been conclusively associated with neurological disease, with de novo variants in individuals with a neurodevelopmental disorder, including a mega corpus callosum. Methods: Using exome sequencing, we identify MAST3 missense variants in individuals with epilepsy. We also assess the effect of these variants on the ability of MAST3 to phosphorylate the target gene product ARPP-16 in HEK293T cells. Results: We identify de novo missense variants in the STK domain in 11 individuals, including 2 recurrent variants p.G510S (n = 5) and p.G515S (n = 3). All 11 individuals had developmental and epileptic encephalopathy, with 8 having normal development prior to seizure onset at \u3c2 years of age. All patients developed multiple seizure types, 9 of 11 patients had seizures triggered by fever and 9 of 11 patients had drug-resistant seizures. In vitro analysis of HEK293T cells transfected with MAST3 cDNA carrying a subset of these patient-specific missense variants demonstrated variable but generally lower expression, with concomitant increased phosphorylation of the MAST3 target, ARPP-16, compared to wild-type. These findings suggest the patient-specific variants may confer MAST3 gain-of-function. Moreover, single-nuclei RNA sequencing and immunohistochemistry shows that MAST3 expression is restricted to excitatory neurons in the cortex late in prenatal development and postnatally. Interpretation: In summary, we describe MAST3 as a novel epilepsy-associated gene with a potential gain-of-function pathogenic mechanism that may be primarily restricted to excitatory neurons in the cortex. ANN NEUROL 2021;90:274–284

Global patient outcomes after elective surgery: prospective cohort study in 27 low-, middle- and high-income countries.

BACKGROUND: As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. METHODS: We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary outcome was in-hospital complications. Secondary outcomes were death following a complication (failure to rescue) and death in hospital. Process measures were admission to critical care immediately after surgery or to treat a complication and duration of hospital stay. A single definition of critical care was used for all countries. RESULTS: A total of 474 hospitals in 19 high-, 7 middle- and 1 low-income country were included in the primary analysis. Data included 44 814 patients with a median hospital stay of 4 (range 2-7) days. A total of 7508 patients (16.8%) developed one or more postoperative complication and 207 died (0.5%). The overall mortality among patients who developed complications was 2.8%. Mortality following complications ranged from 2.4% for pulmonary embolism to 43.9% for cardiac arrest. A total of 4360 (9.7%) patients were admitted to a critical care unit as routine immediately after surgery, of whom 2198 (50.4%) developed a complication, with 105 (2.4%) deaths. A total of 1233 patients (16.4%) were admitted to a critical care unit to treat complications, with 119 (9.7%) deaths. Despite lower baseline risk, outcomes were similar in low- and middle-income compared with high-income countries. CONCLUSIONS: Poor patient outcomes are common after inpatient surgery. Global initiatives to increase access to surgical treatments should also address the need for safe perioperative care. STUDY REGISTRATION: ISRCTN5181700