Canonical matrices of bilinear and sesquilinear forms

Canonical matrices are given for (a) bilinear forms over an algebraically closed or real closed field; (b) sesquilinear forms over an algebraically closed field and over real quaternions with any nonidentity involution; and (c) sesquilinear forms over a field F of characteristic different from 2 with involution (possibly, the identity) up to classification of Hermitian forms over finite extensions of F. A method for reducing the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings is used to construct the canonical matrices. This method has its origins in representation theory and was devised in [V.V. Sergeichuk, Math. USSR-Izv. 31 (1988) 481-501].Comment: 44 pages; misprints corrected; accepted for publication in Linear Algebra and its Applications (2007

Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras

This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice), reflection group $W\subset W(S)$, fundamental polyhedron \Cal M of $W$ and an acceptable (corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors orthogonal to faces of \Cal M (simple roots). One can construct the corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by $M$. We show that \goth g has good behavior of imaginary roots, its denominator formula is defined in a natural domain and has good automorphic properties if and only if \goth g has so called {\it restricted arithmetic type}. We show that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus, Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a natural class to study. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the best automorphic properties for the denominator function if they have {\it a lattice Weyl vector $\rho$}. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type with generalized lattice Weyl vector $\rho$ are called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on results and ideas. 31 pages, no figures. AMSTe

Program Comprehension: Identifying Learning Trajectories for Novice Programmers

This working group asserts that Program Comprehension (PC) plays a critical part in the writing process. For example, this abstract is written from a basic draft that we have edited and revised until it clearly presents our idea. Similarly, a program is written in an incremental manner, with each step being tested, debugged and extended until the program achieves its goal. Novice programmers should develop their program comprehen- sion as they learn to code, so that they are able to read and reason about code while they are writing it. To foster such competencies our group has identified two main goals: (1) to collect and define learning activities that explicitly cover key components of program comprehension and (2) to define possible learning trajectories that will guide teachers using those learning activities in their CS0/CS1 or K-12 courses. [...

Canonical matrices of isometric operators on indefinite inner product spaces

We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay)=B(x,y) on a vector space over F in the following cases: (i) F is an algebraically closed field of characteristic different from 2 or a real closed field, and B is symmetric or skew-symmetric; (ii) F is an algebraically closed field or the skew field of quaternions over a real closed field, and B is Hermitian or skew-Hermitian with respect to any nonidentity involution on F. We use a method that admits to reduce the problem of classifying an arbitrary system of forms and linear mappings to the problem of classifying representations of some quiver. This method was described in [V.V. Sergeichuk, Math. USSR-Izv. 31 (1988) 481-501].Comment: 57 page

Top-down contingent feature-specific orienting with and without awareness of the visual input

In the present article, the role of endogenous feature-specific orienting for conscious and unconscious vision is reviewed. We start with an overview of orienting. We proceed with a review of masking research, and the definition of the criteria of experimental protocols that demonstrate endogenous and exogenous orienting, respectively. Against this background of criteria, we assess studies of unconscious orienting and come to the conclusion that so far studies of unconscious orienting demonstrated endogenous feature-specific orienting. The review closes with a discussion of the role of unconscious orienting in action control

Binding binding: Departure points for a different version of the perceptual retouch theory

In the perceptual retouch theory, masking and related microgenetic phenomena were explained as a result of interaction between specific cortical representational systems and the non-specific sub-cortical modulation system. Masking appears as deprivation of sufficient modulation of the consciousness mechanism suffered by the target-specific signals because of the temporal delay of non-specific modulation (necessary for conscious representation), which explicates the later-coming mask information instead of the already decayed target information. The core of the model envisaged relative magnitudes of EPSPs of single cortical cells driven by target and mask signals at the moment when the nonspecific, presynaptic, excitatory input arrives from the thalamus. In the light of the current evidence about the importance of synchronised activity of specific and non-specific systems in generating consciousness, the retouch theory requires perhaps a different view. This article presents some premises for modification of the retouch theory, where instead of the cumulative presynaptic spike activities and EPSPs of single cells, the oscillatory activity in the gamma range of the participating systems is considered and shown to be consistent with the basic ideas of the retouch theory. In this conceptualisation, O-binding refers to specific encoding which is based on gamma-band synchronised oscillations in the activity of specific cortical sensory modules that represent features and objects; C-binding refers to the gamma-band oscillations in the activity of the non-specific thalamic systems, which is necessary for the O-binding based data to become consciously experienced

Zinc Sensing Receptor Signaling, Mediated by GPR39, Reduces Butyrate-Induced Cell Death in HT29 Colonocytes via Upregulation of Clusterin

Zinc enhances epithelial proliferation, protects the digestive epithelial layer and has profound antiulcerative and antidiarrheal roles in the colon. Despite the clinical significance of this ion, the mechanisms linking zinc to these cellular processes are poorly understood. We have previously identified an extracellular Zn2+ sensing G-protein coupled receptor (ZnR) that activates Ca2+ signaling in colonocytes, but its molecular identity as well as its effects on colonocytes' survival remained elusive. Here, we show that Zn2+, by activation of the ZnR, protects HT29 colonocytes from butyrate induced cell death. Silencing of the G-protein coupled receptor GPR39 expression abolished ZnR-dependent Ca2+ release and Zn2+-dependent survival of butyrate-treated colonocytes. Importantly, GPR39 also mediated ZnR-dependent upregulation of Na+/H+ exchange activity as this activity was found in native colon tissue but not in tissue obtained from GPR39 knock-out mice. Although ZnR-dependent upregulation of Na+/H+ exchange reduced the cellular acid load induced by butyrate, it did not rescue HT29 cells from butyrate induced cell death. ZnR/GPR39 activation however, increased the expression of the anti-apoptotic protein clusterin in butyrate-treated cells. Furthermore, silencing of clusterin abolished the Zn2+-dependent survival of HT29 cells. Altogether, our results demonstrate that extracellular Zn2+, acting through ZnR, regulates intracellular pH and clusterin expression thereby enhancing survival of HT29 colonocytes. Moreover, we identify GPR39 as the molecular moiety of ZnR in HT29 and native colonocytes

Neuro-cognitive mechanisms of conscious and unconscious visual perception: From a plethora of phenomena to general principles

Psychological and neuroscience approaches have promoted much progress in elucidating the cognitive and neural mechanisms that underlie phenomenal visual awareness during the last decades. In this article, we provide an overview of the latest research investigating important phenomena in conscious and unconscious vision. We identify general principles to characterize conscious and unconscious visual perception, which may serve as important building blocks for a unified model to explain the plethora of findings. We argue that in particular the integration of principles from both conscious and unconscious vision is advantageous and provides critical constraints for developing adequate theoretical models. Based on the principles identified in our review, we outline essential components of a unified model of conscious and unconscious visual perception. We propose that awareness refers to consolidated visual representations, which are accessible to the entire brain and therefore globally available. However, visual awareness not only depends on consolidation within the visual system, but is additionally the result of a post-sensory gating process, which is mediated by higher-level cognitive control mechanisms. We further propose that amplification of visual representations by attentional sensitization is not exclusive to the domain of conscious perception, but also applies to visual stimuli, which remain unconscious. Conscious and unconscious processing modes are highly interdependent with influences in both directions. We therefore argue that exactly this interdependence renders a unified model of conscious and unconscious visual perception valuable. Computational modeling jointly with focused experimental research could lead to a better understanding of the plethora of empirical phenomena in consciousness research

Target Cueing Provides Support for Target- and Resource-Based Models of the Attentional Blink

The attentional blink (AB) describes a time-based deficit in processing the second of two masked targets. The AB is attenuated if successive targets appear between the first and final target, or if a cueing target is positioned before the final target. Using various speeds of stimulus presentation, the current study employed successive targets and cueing targets to confirm and extend an understanding of target-target cueing in the AB. In Experiment 1, three targets were presented sequentially at rates of 30 msec/item or 90 msec/item. Successive targets presented at 90 msec improved performance compared with non-successive targets. However, accuracy was equivalently high for successive and non-successive targets presented at 30 msec/item, suggesting that–regardless of whether they occurred consecutively–those items fell within the temporally defined attentional window initiated by the first target. Using four different presentation speeds, Experiment 2 confirmed the time-based definition of the AB and the success of target-cueing at 30 msec/item. This experiment additionally revealed that cueing was most effective when resources were not devoted to the cue, thereby implicating capacity limitations in the AB. Across both experiments, a novel order-error measure suggested that errors tend to decrease with an increasing duration between the targets, but also revealed that certain stimulus conditions result in stable order accuracy. Overall, the results are best encapsulated by target-based and resource-sharing theories of the AB, which collectively value the contributions of capacity limitations and optimizing transient attention in time

Human Intestinal Lumen and Mucosa-Associated Microbiota in Patients with Colorectal Cancer

Recent reports have suggested the involvement of gut microbiota in the progression of colorectal cancer (CRC). We utilized pyrosequencing based analysis of 16S rRNA genes to determine the overall structure of microbiota in patients with colorectal cancer and healthy controls; we investigated microbiota of the intestinal lumen, the cancerous tissue and matched noncancerous normal tissue. Moreover, we investigated the mucosa-adherent microbial composition using rectal swab samples because the structure of the tissue-adherent bacterial community is potentially altered following bowel cleansing. Our findings indicated that the microbial structure of the intestinal lumen and cancerous tissue differed significantly. Phylotypes that enhance energy harvest from diets or perform metabolic exchange with the host were more abundant in the lumen. There were more abundant Firmicutes and less abundant Bacteroidetes and Proteobacteria in lumen. The overall microbial structures of cancerous tissue and noncancerous tissue were similar; howerer the tumor microbiota exhibited lower diversity. The structures of the intestinal lumen microbiota and mucosa-adherent microbiota were different in CRC patients compared to matched microbiota in healthy individuals. Lactobacillales was enriched in cancerous tissue, whereas Faecalibacterium was reduced. In the mucosa-adherent microbiota, Bifidobacterium, Faecalibacterium, and Blautia were reduced in CRC patients, whereas Fusobacterium, Porphyromonas, Peptostreptococcus, and Mogibacterium were enriched. In the lumen, predominant phylotypes related to metabolic disorders or metabolic exchange with the host, Erysipelotrichaceae, Prevotellaceae, and Coriobacteriaceae were increased in cancer patients. Coupled with previous reports, these results suggest that the intestinal microbiota is associated with CRC risk and that intestinal lumen microflora potentially influence CRC risk via cometabolism or metabolic exchange with the host. However, mucosa-associated microbiota potentially affects CRC risk primarily through direct interaction with the host