k is the Magic Number -- Inferring the Number of Clusters Through Nonparametric Concentration Inequalities

Most convex and nonconvex clustering algorithms come with one crucial parameter: the $k$ in $k$-means. To this day, there is not one generally accepted way to accurately determine this parameter. Popular methods are simple yet theoretically unfounded, such as searching for an elbow in the curve of a given cost measure. In contrast, statistically founded methods often make strict assumptions over the data distribution or come with their own optimization scheme for the clustering objective. This limits either the set of applicable datasets or clustering algorithms. In this paper, we strive to determine the number of clusters by answering a simple question: given two clusters, is it likely that they jointly stem from a single distribution? To this end, we propose a bound on the probability that two clusters originate from the distribution of the unified cluster, specified only by the sample mean and variance. Our method is applicable as a simple wrapper to the result of any clustering method minimizing the objective of $k$-means, which includes Gaussian mixtures and Spectral Clustering. We focus in our experimental evaluation on an application for nonconvex clustering and demonstrate the suitability of our theoretical results. Our \textsc{SpecialK} clustering algorithm automatically determines the appropriate value for $k$, without requiring any data transformation or projection, and without assumptions on the data distribution. Additionally, it is capable to decide that the data consists of only a single cluster, which many existing algorithms cannot

A Novel Approach for Ellipsoidal Outer-Approximation of the Intersection Region of Ellipses in the Plane

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are determined, and a set of points is generated on the elliptic arcs connecting every two neighbouring intersection points. By finding the tangent lines to the ellipses at the extended set of points, a set of half-planes is obtained, whose intersection forms a polygon. To find the polygon more efficiently, the points are given an order and the intersection of the half-planes corresponding to every two neighbouring points is calculated. If the polygon is convex and bounded, these calculated points together with the initially obtained intersection points will form its vertices. If the polygon is non-convex or unbounded, we can detect this situation and then generate additional discrete points only on the elliptical arc segment causing the issue, and restart the algorithm to obtain a bounded and convex polygon. Finally, the smallest area ellipse that contains the vertices of the polygon is obtained by solving a convex optimization problem. Through numerical experiments, it is illustrated that the proposed technique returns a tighter outer-approximation of the intersection of multiple ellipses, compared to conventional techniques, with only slightly higher computational cost

An improved methodology for the recovery of Zea mays and other large crop pollen, with implications for environmental archaeology in the Neotropics

We present a simple sieving methodology to aid the recovery of large cultigen pollen grains, such as maize (Zea mays L.), manioc (Manihot esculenta Crantz), and sweet potato (Ipomoea batatas L.), among others, for the detection of food production using fossil pollen analysis of lake sediments in the tropical Americas. The new methodology was tested on three large study lakes located next to known and/or excavated pre-Columbian archaeological sites in South and Central America. Five paired samples, one treated by sieving, the other prepared using standard methodology, were compared for each of the three sites. Using the new methodology, chemically digested sediment samples were passed through a 53 µm sieve, and the residue was retained, mounted in silicone oil, and counted for large cultigen pollen grains. The filtrate was mounted and analysed for pollen according to standard palynological procedures. Zea mays (L.) was recovered from the sediments of all three study lakes using the sieving technique, where no cultigen pollen had been previously recorded using the standard methodology. Confidence intervals demonstrate there is no significant difference in pollen assemblages between the sieved versus unsieved samples. Equal numbers of exotic Lycopodium spores added to both the filtrate and residue of the sieved samples allow for direct comparison of cultigen pollen abundance with the standard terrestrial pollen count. Our technique enables the isolation and rapid scanning for maize and other cultigen pollen in lake sediments, which, in conjunction with charcoal and pollen records, is key to determining land-use patterns and the environmental impact of pre-Columbian societies

Targeting the X Chromosome during Spermatogenesis Induces Y Chromosome Transmission Ratio Distortion and Early Dominant Embryo Lethality in Anopheles gambiae

We have exploited the high selectivity of the homing endonuclease I-PpoI for the X-linked Anopheles gambiae 28S ribosomal genes to selectively target X chromosome carrying spermatozoa. Our data demonstrated that in heterozygous males, the expression of I-PpoI in the testes induced a strong bias toward Y chromosome–carrying spermatozoa. Notably, these male mosquitoes also induced complete early dominant embryo lethality in crosses with wild-type females. Morphological and molecular data indicated that all spermatozoa, irrespectively of the inheritance of the transgene, carried a substantial amount of I-PpoI protein that could attack the maternally inherited chromosome X of the embryo. Besides the obvious implications for implementing vector control measures, our data demonstrated the feasibility of generating synthetic sex distorters and revealed the intriguing possibility of manipulating maternally inherited genes using wild-type sperm cells carrying engineered endonucleases

Targeting the X Chromosome during Spermatogenesis Induces Y Chromosome Transmission Ratio Distortion and Early Dominant Embryo Lethality in Anopheles gambiae

We have exploited the high selectivity of the homing endonuclease I-PpoI for the X-linked Anopheles gambiae 28S ribosomal genes to selectively target X chromosome carrying spermatozoa. Our data demonstrated that in heterozygous males, the expression of I-PpoI in the testes induced a strong bias toward Y chromosome–carrying spermatozoa. Notably, these male mosquitoes also induced complete early dominant embryo lethality in crosses with wild-type females. Morphological and molecular data indicated that all spermatozoa, irrespectively of the inheritance of the transgene, carried a substantial amount of I-PpoI protein that could attack the maternally inherited chromosome X of the embryo. Besides the obvious implications for implementing vector control measures, our data demonstrated the feasibility of generating synthetic sex distorters and revealed the intriguing possibility of manipulating maternally inherited genes using wild-type sperm cells carrying engineered endonucleases

Mathematical model of a telomerase transcriptional regulatory network developed by cell-based screening: analysis of inhibitor effects and telomerase expression mechanisms

Cancer cells depend on transcription of telomerase reverse transcriptase (TERT). Many transcription factors affect TERT, though regulation occurs in context of a broader network. Network effects on telomerase regulation have not been investigated, though deeper understanding of TERT transcription requires a systems view. However, control over individual interactions in complex networks is not easily achievable. Mathematical modelling provides an attractive approach for analysis of complex systems and some models may prove useful in systems pharmacology approaches to drug discovery. In this report, we used transfection screening to test interactions among 14 TERT regulatory transcription factors and their respective promoters in ovarian cancer cells. The results were used to generate a network model of TERT transcription and to implement a dynamic Boolean model whose steady states were analysed. Modelled effects of signal transduction inhibitors successfully predicted TERT repression by Src-family inhibitor SU6656 and lack of repression by ERK inhibitor FR180204, results confirmed by RT-QPCR analysis of endogenous TERT expression in treated cells. Modelled effects of GSK3 inhibitor 6-bromoindirubin-3′-oxime (BIO) predicted unstable TERT repression dependent on noise and expression of JUN, corresponding with observations from a previous study. MYC expression is critical in TERT activation in the model, consistent with its well known function in endogenous TERT regulation. Loss of MYC caused complete TERT suppression in our model, substantially rescued only by co-suppression of AR. Interestingly expression was easily rescued under modelled Ets-factor gain of function, as occurs in TERT promoter mutation. RNAi targeting AR, JUN, MXD1, SP3, or TP53, showed that AR suppression does rescue endogenous TERT expression following MYC knockdown in these cells and SP3 or TP53 siRNA also cause partial recovery. The model therefore successfully predicted several aspects of TERT regulation including previously unknown mechanisms. An extrapolation suggests that a dominant stimulatory system may programme TERT for transcriptional stability

Acute tumour response to a bispecific Ang-2-VEGF-A antibody: insights from multiparametric MRI and gene expression profiling.

Background To assess antivascular effects, and evaluate clinically translatable magnetic resonance imaging (MRI) biomarkers of tumour response in vivo, following treatment with vanucizumab, a bispecific human antibody against angiopoietin-2 (Ang-2) and vascular endothelial growth factor-A (VEGF-A).Methods Colo205 colon cancer xenografts were imaged before and 5 days after treatment with a single 10 mg kg(-1) dose of either vanucizumab, bevacizumab (anti-human VEGF-A), LC06 (anti-murine/human Ang-2) or omalizumab (anti-human IgE control). Volumetric response was assessed using T2-weighted MRI, and diffusion-weighted, dynamic contrast-enhanced (DCE) and susceptibility contrast MRI used to quantify tumour water diffusivity (apparent diffusion coefficient (ADC), × 10(6) mm(2) s(-1)), vascular perfusion/permeability (K(trans), min(-1)) and fractional blood volume (fBV, %) respectively. Pathological correlates were sought, and preliminary gene expression profiling performed.Results Treatment with vanucizumab, bevacizumab or LC06 induced a significant (P<0.01) cytolentic response compared with control. There was no significant change in tumour ADC in any treatment group. Uptake of Gd-DTPA was restricted to the tumour periphery in all post-treatment groups. A significant reduction in tumour K(trans) (P<0.05) and fBV (P<0.01) was determined 5 days after treatment with vanucizumab only. This was associated with a significant (P<0.05) reduction in Hoechst 33342 uptake compared with control. Gene expression profiling identified 20 human genes exclusively regulated by vanucizumab, 6 of which are known to be involved in vasculogenesis and angiogenesis.Conclusions Vanucizumab is a promising antitumour and antiangiogenic treatment, whose antivascular activity can be monitored using DCE and susceptibility contrast MRI. Differential gene expression in vanucizumab-treated tumours is regulated by the combined effect of Ang-2 and VEGF-A inhibition

The Effect of Diet and Opponent Size on Aggressive Interactions Involving Caribbean Crazy Ants (Nylanderia fulva)

Biotic interactions are often important in the establishment and spread of invasive species. In particular, competition between introduced and native species can strongly influence the distribution and spread of exotic species and in some cases competition among introduced species can be important. The Caribbean crazy ant, Nylanderia fulva, was recently introduced to the Gulf Coast of Texas, and appears to be spreading inland. It has been hypothesized that competition with the red imported fire ant, Solenopsis invicta, may be an important factor in the spread of crazy ants. We investigated the potential of interspecific competition among these two introduced ants by measuring interspecific aggression between Caribbean crazy ant workers and workers of Solenopsis invicta. Specifically, we examined the effect of body size and diet on individual-level aggressive interactions among crazy ant workers and fire ants. We found that differences in diet did not alter interactions between crazy ant workers from different nests, but carbohydrate level did play an important role in antagonistic interactions with fire ants: crazy ants on low sugar diets were more aggressive and less likely to be killed in aggressive encounters with fire ants. We found that large fire ants engaged in fewer fights with crazy ants than small fire ants, but fire ant size affected neither fire ant nor crazy ant mortality. Overall, crazy ants experienced higher mortality than fire ants after aggressive encounters. Our findings suggest that fire ant workers might outcompete crazy ant workers on an individual level, providing some biotic resistance to crazy ant range expansion. However, this resistance may be overcome by crazy ants that have a restricted sugar intake, which may occur when crazy ants are excluded from resources by fire ants

Quality-of-life assessment in dementia: the use of DEMQOL and DEMQOL-Proxy total scores

Purpose There is a need to determine whether health-related quality-of-life (HRQL) assessments in dementia capture what is important, to form a coherent basis for guiding research and clinical and policy decisions. This study investigated structural validity of HRQL assessments made using the DEMQOL system, with particular interest in studying domains that might be central to HRQL, and the external validity of these HRQL measurements. Methods HRQL of people with dementia was evaluated by 868 self-reports (DEMQOL) and 909 proxy reports (DEMQOL-Proxy) at a community memory service. Exploratory and confirmatory factor analyses (EFA and CFA) were conducted using bifactor models to investigate domains that might be central to general HRQL. Reliability of the general and specific factors measured by the bifactor models was examined using omega (?) and omega hierarchical (? h) coefficients. Multiple-indicators multiple-causes models were used to explore the external validity of these HRQL measurements in terms of their associations with other clinical assessments. Results Bifactor models showed adequate goodness of fit, supporting HRQL in dementia as a general construct that underlies a diverse range of health indicators. At the same time, additional factors were necessary to explain residual covariation of items within specific health domains identified from the literature. Based on these models, DEMQOL and DEMQOL-Proxy overall total scores showed excellent reliability (? h > 0.8). After accounting for common variance due to a general factor, subscale scores were less reliable (? h < 0.7) for informing on individual differences in specific HRQL domains. Depression was more strongly associated with general HRQL based on DEMQOL than on DEMQOL-Proxy (?0.55 vs ?0.22). Cognitive impairment had no reliable association with general HRQL based on DEMQOL or DEMQOL-Proxy. Conclusions The tenability of a bifactor model of HRQL in dementia suggests that it is possible to retain theoretical focus on the assessment of a general phenomenon, while exploring variation in specific HRQL domains for insights on what may lie at the ‘heart’ of HRQL for people with dementia. These data suggest that DEMQOL and DEMQOL-Proxy total scores are likely to be accurate measures of individual differences in HRQL, but that subscale scores should not be used. No specific domain was solely responsible for general HRQL at dementia diagnosis. Better HRQL was moderately associated with less depressive symptoms, but this was less apparent based on informant reports. HRQL was not associated with severity of cognitive impairment