Parametric Polyhedra with at least kk Lattice Points: Their Semigroup Structure and the k-Frobenius Problem

Given an integral $d \times n$ matrix $A$, the well-studied affine semigroup \mbox{ Sg} (A)=\{ b : Ax=b, \ x \in {\mathbb Z}^n, x \geq 0\} can be stratified by the number of lattice points inside the parametric polyhedra $P_A(b)=\{x: Ax=b, x\geq0\}$. Such families of parametric polyhedra appear in many areas of combinatorics, convex geometry, algebra and number theory. The key themes of this paper are: (1) A structure theory that characterizes precisely the subset \mbox{ Sg}_{\geq k}(A) of all vectors b \in \mbox{ Sg}(A) such that $P_A(b) \cap {\mathbb Z}^n$ has at least $k$ solutions. We demonstrate that this set is finitely generated, it is a union of translated copies of a semigroup which can be computed explicitly via Hilbert bases computations. Related results can be derived for those right-hand-side vectors $b$ for which $P_A(b) \cap {\mathbb Z}^n$ has exactly $k$ solutions or fewer than $k$ solutions. (2) A computational complexity theory. We show that, when $n$, $k$ are fixed natural numbers, one can compute in polynomial time an encoding of \mbox{ Sg}_{\geq k}(A) as a multivariate generating function, using a short sum of rational functions. As a consequence, one can identify all right-hand-side vectors of bounded norm that have at least $k$ solutions. (3) Applications and computation for the $k$-Frobenius numbers. Using Generating functions we prove that for fixed $n,k$ the $k$-Frobenius number can be computed in polynomial time. This generalizes a well-known result for $k=1$ by R. Kannan. Using some adaptation of dynamic programming we show some practical computations of $k$-Frobenius numbers and their relatives

Long time dynamics and coherent states in nonlinear wave equations

We discuss recent progress in finding all coherent states supported by nonlinear wave equations, their stability and the long time behavior of nearby solutions.Comment: bases on the authors presentation at 2015 AMMCS-CAIMS Congress, to appear in Fields Institute Communications: Advances in Applied Mathematics, Modeling, and Computational Science 201

Effects of Epitope Modification on T Cell Receptor–Ligand Binding and Antigen Recognition by Seven H-2Kd–restricted Cytotoxic T Lymphocyte Clones Specific for a Photoreactive Peptide Derivative

We tested for antigen recognition and T cell receptor (TCR)–ligand binding 12 peptide derivative variants on seven H-2Kd–restricted cytotoxic T lymphocytes (CTL) clones specific for a bifunctional photoreactive derivative of the Plasmodium berghei circumsporozoite peptide 252– 260 (SYIPSAEKI). The derivative contained iodo-4-azidosalicylic acid in place of PbCS S-252 and 4-azidobenzoic acid on PbCS K-259. Selective photoactivation of the N-terminal photoreactive group allowed crosslinking to Kd molecules and photoactivation of the orthogonal group to TCR. TCR photoaffinity labeling with covalent Kd–peptide derivative complexes allowed direct assessment of TCR–ligand binding on living CTL. In most cases (over 80%) cytotoxicity (chromium release) and TCR–ligand binding differed by less than fivefold. The exceptions included (a) partial TCR agonists (8 cases), for which antigen recognition was fivetenfold less efficient than TCR–ligand binding, (b) TCR antagonists (2 cases), which were not recognized and capable of inhibiting recognition of the wild-type conjugate, (c) heteroclitic agonists (2 cases), for which antigen recognition was more efficient than TCR–ligand binding, and (d) one partial TCR agonist, which activated only Fas (CD95), but not perforin/granzymemediated cytotoxicity. There was no correlation between these divergences and the avidity of TCR–ligand binding, indicating that other factors than binding avidity determine the nature of the CTL response. An unexpected and novel finding was that CD8-dependent clones clearly incline more to TCR antagonism than CD8-independent ones. As there was no correlation between CD8 dependence and the avidity of TCR–ligand binding, the possibility is suggested that CD8 plays a critical role in aberrant CTL function

The effect of autonomy, training opportunities, age and salaries on job satisfaction in the South East Asian retail petroleum industry

South East Asian petroleum retailers are under considerable pressure to improve service quality by reducing turnover. An empirical methodology from this industry determined the extent to which job characteristics, training opportunities, age and salary influenced the level of job satisfaction, an indicator of turnover. Responses are reported on a random sample of 165 site employees (a 68% response rate) of a Singaporean retail petroleum firm. A restricted multivariate regression model of autonomy and training opportunities explained the majority (35.4%) of the variability of job satisfaction. Age did not moderate these relationships, except for employees >21 years of age, who reported enhanced job satisfaction with additional salary. Human Capital theory, Life Cycle theory and Job Enrichment theory are invoked and explored in the context of these findings in the South East Asian retail petroleum industry. In the South East Asian retail petroleum industry, jobs providing employees with the opportunity to undertake a variety of tasks that enhanced the experienced meaningfulness of work are likely to promote job satisfaction, reduce turnover and increase the quality of service

Cross-ancestry genome-wide association analysis of corneal thickness strengthens link between complex and Mendelian eye diseases

Central corneal thickness (CCT) is a highly heritable trait associated with complex eye diseases such as keratoconus and glaucoma. We perform a genome-wide association meta-analysis of CCT and identify 19 novel regions. In addition to adding support for known connective tissue-related pathways, pathway analyses uncover previously unreported gene sets. Remarkably, >20% of the CCT-loci are near or within Mendelian disorder genes. These included FBN1, ADAMTS2 and TGFB2 which associate with connective tissue disorders (Marfan, Ehlers-Danlos and Loeys-Dietz syndromes), and the LUM-DCN-KERA gene complex involved in myopia, corneal dystrophies and cornea plana. Using index CCT-increasing variants, we find a significant inverse correlation in effect sizes between CCT and keratoconus (r =-0.62, P = 5.30 × 10-5) but not between CCT and primary open-angle glaucoma (r =-0.17, P = 0.2). Our findings provide evidence for shared genetic influences between CCT and keratoconus, and implicate candidate genes acting in collagen and extracellular matrix regulation

Editorial Statement About JCCAP’s 2023 Special Issue on Informant Discrepancies in Youth Mental Health Assessments: Observations, Guidelines, and Future Directions Grounded in 60 Years of Research

Issue 1 of the 2011 Volume of the Journal of Clinical Child and Adolescent Psychology (JCCAP) included a Special Section about the use of multi-informant approaches to measure child and adolescent (i.e., hereafter referred to collectively as “youth”) mental health (De Los Reyes, 2011). Researchers collect reports from multiple informants or sources (e.g., parent and peer, youth and teacher) to estimate a given youth’s mental health. The 2011 JCCAP Special Section focused on the most common outcome of these approaches, namely the significant discrepancies that arise when comparing estimates from any two informant’s reports (i.e., informant discrepancies). These discrepancies appear in assessments conducted across the lifespan (Achenbach, 2020). That said, JCCAP dedicated space to understanding informant discrepancies, because they have been a focus of scholarship in youth mental health for over 60 years (e.g., Achenbach et al., 1987; De Los Reyes & Kazdin, 2005; Glennon & Weisz, 1978; Kazdin et al., 1983; Kraemer et al., 2003; Lapouse & Monk, 1958; Quay et al., 1966; Richters, 1992; Rutter et al., 1970; van der Ende et al., 2012). Thus, we have a thorough understanding of the areas of research for which they reliably appear when clinically assessing youth. For instance, intervention researchers observe informant discrepancies in estimates of intervention effects within randomized controlled trials (e.g., Casey & Berman, 1985; Weisz et al., 2017). Service providers observe informant discrepancies when working with individual clients, most notably when making decisions about treatment planning (e.g., Hawley & Weisz, 2003; Hoffman & Chu, 2015). Scholars in developmental psychopathology observe these discrepancies when seeking to understand risk and protective factors linked to youth mental health concerns (e.g., Hawker & Boulton, 2000; Hou et al., 2020; Ivanova et al., 2022). Thus, the 2011 JCCAP Special Section posed a question: Might these informant discrepancies contain data relevant to understanding youth mental health? Suppose none of the work in youth mental health is immune from these discrepancies. In that case, the answer to this question strikes at the core of what we produce―from the interventions we develop and implement, to the developmental psychopathology research that informs intervention development