We investigate the question of whether a simple closed curve in the plane must contain all four vertices of some rhombus having one diagonal collinear with a specified point. This complements previous research on whether there is a rhombus with a diagonal or side parallel to a given line. We obtain a new proof that a simple closed curve contains the vertices of uncountably many rhombi. We also explore conditions guaranteeing that all points in some region are collinear with diagonals of such rhombi.

High-throughput screening, in which large numbers of compounds are traditionally studied one-at-a-time in multiwell plates against specific targets, is widely used across many areas of the biological sciences, including drug discovery. To improve the effectiveness of these screens, we propose a new class of supersaturated designs that guide the construction of pools of compounds in each well. Because the size of the pools is typically limited by the particular application, the new designs accommodate this constraint and are part of a larger procedure that we call Constrained Row Screening or CRowS. We develop an efficient computational procedure to construct the CRowS designs, provide some initial lower bounds on the average squared off-diagonal values of their main-effects information matrix, and study the impact of the constraint on design quality. We also show via simulation that CRowS is statistically superior to the traditional one-compound-one-well approach as well as an existing pooling method, and demonstrate the use of the new methodology on a Verona Integron-encoded Metallo-$\beta$-lactamase-2 assay.

A finite-step procedure is proposed for maximum likelihood estimation of the three-parameter asymmetric Laplace distribution. Its performance is compared with the iterative method most commonly used for this distribution. The new procedure is much faster and reliably identifies samples for which maximum likelihood estimates lie on the boundary of the parameter space, making it a good choice for simulation studies and simulation-based methodologies.

We present a complete constructive proof of the classical mountain-climbing theorem for two continuous piecewise monotone profiles. The proof strengthens the classical result, fills gaps omitted by previous proofs, provides information relevant to computational complexity, and illuminates how special properties of the separate profiles may be reflected in the functions that coordinate the movements of the two climbers.

Recent research has shown that very large convex transportation problems can be solved efficiently with interior point methods by finding a good pre-conditioner for an iterative linear-equation solver. In this article, it is demonstrated that the specific structure of the constraints allows use of a direct method for solving those linear equations with the same order of worst-case time complexity.

A characterization of idempotency is given for triangular matrices with entries from an arbitrary ring. This yields an elementary approach to constructing such matrices. It also reveals structure allowing for the explicit enumeration or implicit counting of all idempotent triangular matrices over a given finite ring.

Von Neumann regularity within a ring of upper triangular matrices is characterized in terms of how such a matrix and an upper triangular generalized inverse can be constructed. In the case of a finite ring, this yields a method for implicitly counting all upper triangular matrices that admit upper triangular generalized inverses.

A major contributing factor in triple-negative breast cancer progression is its ability to evade immune surveillance. One mechanism for this immunosuppression is through ribosomal protein S19 (RPS19), which facilitates myeloid-derived suppressor cells (MDSCs) recruitment in tumors, which generate cytokines TGF-β and IL-10 and induce regulatory T cells (Tregs), all of which are immunosuppressive and enhance tumor progression. Hence, enhancing the immune system in breast tumors could be a strategy for anticancer therapeutics. The present study evaluated the immune response of atovaquone, an antiprotozoal drug, in three independent breast-tumor models. Our results demonstrated that oral administration of atovaquone reduced HCC1806, CI66 and 4T1 paclitaxel-resistant (4T1-PR) breast-tumor growth by 45%, 70% and 42%, respectively. MDSCs, TGF-β, IL-10 and Tregs of blood and tumors were analyzed from all of these in vivo models. Our results demonstrated that atovaquone treatment in mice bearing HCC1806 tumors reduced MDSCs from tumor and blood by 70% and 30%, respectively. We also observed a 25% reduction in tumor MDSCs in atovaquone-treated mice bearing CI66 and 4T1-PR tumors. In addition, a decrease in TGF-β and IL-10 in tumor lysates was observed in atovaquone-treated mice with a reduction in tumor Tregs. Moreover, a significant reduction in the expression of RPS19 was found in tumors treated with atovaquone.

Efficient methods for convex resource allocation problems usually exploit algebraic properties of the objective function. For problems with nested constraints, we show that constraint sparsity structure alone allows rapid solution with a general interior point method. The key is a special-purpose linear system solver requiring only linear time in the problem dimensions. Computational tests show that this approach outperforms the previous best algebraically specialized methods.

Cytotoxic T-lymphocyte activation and extension of the cell life span is necessary in order to enable immunotherapy to perform effectively against cancer. In the present study, mucin 1 (MUC1)-stimulated human mononuclear cells (M1SHMCs) were costimulated with bead-attached monoclonal antibodies specific for cluster of differentiation (CD)3 and CD28 receptors. The study was undertaken to determine whether costimulation was capable of enhancing the killing of cancer cells in vitro and of protecting non-obese diabetic severe combined immunodeficient mice from tumor development. Lysis of MCF-7 tumor cells by M1SHMCs was reduced following costimulation with anti-CD3 and anti-CD28. Furthermore, costimulation with anti-CD3 and anti-CD28 eliminated the protective effects of M1SHMCs on MCF-7 breast cancer cell growth in the non-obese diabetic severe combined immunodeficient mice. The present study suggested that costimulation with anti-CD3 and anti-CD28 is not advisable following antigen activation of lymphocytes under the conditions used here. Using a lower anti-CD3/CD28 bead to T-cell ratio may prevent immune suppression, however, further studies are required to support this hypothesis.

We present an integer linear programming formulation and solution procedure for determining the tightest bounds on cell counts in a multi-way contingency table, given knowledge of a corresponding derived two-way table of rounded conditional probabilities and the sample size. The problem has application in statistical disclosure limitation, which is concerned with releasing useful data to the public and researchers while also preserving privacy and confidentiality. Previous work on this problem invoked the simplifying assumption that the conditionals were released as fractions in lowest terms, rather than the more realistic and complicated setting of rounded decimal values that is treated here. The proposed procedure finds all possible counts for each cell and runs fast enough to handle moderately sized tables. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

Breast tumors are heterogeneous with a complex etiology. The immune system plays a crucial role in the development of tumors and can facilitate tumor growth pleiotropically. Myeloid derived suppressor cells (MDSCs) generate reactive oxygen species (ROS) and cytokines to suppress T cells, dendritic cells and natural killer (NK) cells. Hence, the inhibition of MDSCs could be an important strategy for anticancer therapeutics. Phenethyl isothiocyanate (PEITC), a bioactive compound present in cruciferous vegetables, is known to have anticancer properties. However, the effects of PEITC administration on the immune system have not been previously reported. In the current study, we evaluated the effects of administering PEITC to immunocompromised NOD-SCID IL2R gamma(-/-) (SCID/NSG) host mice bearing MDA-MB-231 xenografts on MDSCs in the peripheral blood. Our results reveal that oral administration of 12 mu mol PEITC attenuated tumor growth by 76%. This was marked tumor-inhibitory phenotype was associated with a significant reduction in the levels of MDSCs bearing the surface markers CD33, CD34 and CD11b in PEITC treated mice, indicating that overall tumor growth suppression by PEITC correlates with inhibition of MDSCs. To the best of our knowledge, this is the first study showing effects of PEITC on MDSCs.

Recent research has raised questions about the structure and calculation of bounds on the underlying cell counts for a contingency table released in the form of conditional probabilities. This problem has implications for statistical disclosure limitation. We elucidate the mathematical structure of the problem in fairly elementary terms, under the assumption that the unrounded conditionals and sample size are known. To do so, we reformulate a standard integer programming approach as a knapsack problem, show that this provides many insights into the problem, and provide illustrations in the context of several datasets. In particular, we demonstrate that the tightest bounds are much easier to calculate than previously believed, and we also identify circumstances in which disclosure is either guaranteed or unlikely to occur.

Resource allocation problems are usually solved with specialized methods exploiting their general sparsity and problem-specific algebraic structure. We show that the sparsity structure alone yields a closed-form Newton search direction for the generic primal-dual interior point method. Computational tests show that the interior point method consistently outperforms the best specialized methods when no additional algebraic structure is available.

The aim of the present study was to determine whether the combination of two modalities of immunotherapy, targeting two different tumor antigens, may be feasible and non-toxic, yet enhance the killing of a human breast cancer cell line. The first modality was tumor growth factor α-Pseudomonas exotoxin 38 (TGFα-PE38), which specifically targets and kills tumor cells that express the epidermal growth factor receptor. The second modality was mucin-1 (MUC1)-specific cytotoxic T lymphocytes (CTLs), generated by MUC1 stimulation of peripheral blood mononuclear cells, to target the human breast cancer cell line, MCF7. TGFα-PE38 exhibited specific lysis of the MCF7 cells in a concentration- and time-dependent manner. TGFα-PE38 did not kill the normal hematopoietic stem cells or CTLs. Furthermore, TGFα-PE38 was not inhibitory for the growth or differentiation of the normal human hematopoietic stem cells into erythroid and myeloid colonies. In addition, TGFα-PE38 did not inhibit the killing function of CTLs, either when preincubated or co-incubated with CTLs. Finally, therapeutic enhancement was observed, in that TGFα-PE38 and CTLs were additive in the specific lysis of the MCF7 cells. These two modalities of immunotherapy may be beneficial for humans with breast cancer with or without other therapies, including autologous hematopoietic stem cell transplantation, specifically for purging cancer cells from hematopoietic stem cells prior to transplantation.

We present a fast method for determining the tightest possible bounds, as well as all feasible values, for the underlying cell counts in a two-way contingency table based on knowledge of the corresponding unrounded conditional probabilities, the sample size, and (optionally) bounds on cells and certain sums of cells. This information can be used in statistical inference procedures and also has potential uses in statistical disclosure control, which deals with protecting privacy and confidentiality when data summaries are released to the public. The problem formally consists of a large number of integer linear knapsack optimizations (two per cell). Here we identify special common structure that allows for efficient reuse among cells of intermediate results within a dynamic programming framework. The method runs very quickly on practical examples, thereby enabling a real-time interactive exploration of disclosure risk for two-way rearrangements of large multi-way tables.

The epidemiological evidence suggests a strong inverse relationship between dietary intake of cruciferous vegetables and the incidence of cancer. Among other constituents of cruciferous vegetables, isothiocyanates (ITC) are the main bioactive chemicals present. Phenethyl isothiocyanate (PEITC) is present as gluconasturtiin in many cruciferous vegetables with remarkable anti-cancer effects. PEITC is known to not only prevent the initiation phase of carcinogenesis process but also to inhibit the progression of tumorigenesis. PEITC targets multiple proteins to suppress various cancer-promoting mechanisms such as cell proliferation, progression and metastasis. Pre-clinical evidence suggests that combination of PEITC with conventional anti-cancer agents is also highly effective in improving overall efficacy. Based on accumulating evidence, PEITC appears to be a promising agent for cancer therapy and is already under clinical trials for leukemia and lung cancer. This is the first review which provides a comprehensive analysis of known targets and mechanisms along with a critical evaluation of PEITC as a future anti-cancer agent.

Dendritic cells (DCs) are among the most potent antigen-presenting cells (APCs), stimulating peripheral blood mononuclear cells (PBMCs) to generate antigen-specific cytotoxic T lymphocytes (CTLs). The objectives of this study were to determine if interleukin (IL)-4 is beneficial or detrimental for the generation of human DCs in vitro and to understand whether DCs generated in vitro in the presence or absence of IL-4 stimulate the killing of adenocarcinoma cells by CTLs in vivo. Mucin 1 (MUC1), a glycoprotein found on the surface of adenocarcinoma cells was used to load DCs. MUC1-loaded DCs generated in the absence of IL-4 were superior to their counterparts produced with IL-4 in stimulating PBMCs to kill human breast cancer MCF-7 cells in vitro. A corollary in vivo protection experiment was performed by injecting immunodeficient NOD-SCID mice with MCF-7 cells s.c. and MUC1-loaded CTLs, PBMCs, or DCs generated in the absence of IL-4, i.p. Mice that received CTLs and MUC1-loaded DCs on days 0, 2, 4, 9, 14 and 19 were completely protected against the development of MCF-7-derived tumors, while other schedules conferred lower protection. Therefore, tumor antigen-loaded DCs enhance the efficacy of adoptive CTL transfer, and should thus be considered for combinatorial immunotherapeutic regimens.

In this paper, we obtain estimates for the contingent and adjacent derivatives of the epigraph of the marginal multifunction in parametric set-valued optimization. These estimates generalize some sensitivity results from scalar-valued optimization and provide new information in the setting of multiobjective nonlinear programming.

Interaction between antigen presenting cells and T lymphocytes, through receptors and co-stimulatory molecules present on the surface of these cells, is one of the key means to modulate the adaptive immune system. Tucaresol, a Schiff-base-forming chemical, can be used as a substitute for the physiological donor of carbonyl groups of antigen presenting cells, which can interact with the amine groups of T lymphocytes to modulate the adaptive immune system. This study was done to determine whether tucaresol can enhance killing of cancer cells in vitro as well as protect non-obese diabetic severe combined immunodeficient mice from tumor development by mucin 1 stimulated human mononuclear cells through the adaptive immune system. The expected hypothesis was not supported. Percent specific lysis of MCF-7 tumor cells by mucin 1 stimulated human mononuclear cells was reduced by tucaresol. Furthermore, tucaresol abolished the protective effect of mucin 1 stimulated human mononuclear cells against MCF-7 breast cancer cell growth in non-obese diabetic severe combined immunodeficient mice. This study implies that tucaresol may be of use as an immunosuppressive agent.