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The Mycielskian construction, denoted μ(G), takes a finite simple graph G to a larger graph with of the same clique number but larger chromatic number. The generalized Mycielskian construction, denoted μt(G), takes G to a larger graph with the same chromatic number but with larger odd girth. In this chapter we look at symmetry parameters of μ(G) and μt(G) in terms of the same parameters of G. These symmetry parameters include determining number, distinguishing number, and cost of distinguishing.

A set $S$ of vertices is a determining set for a graph $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The size of a smallest determining set for $G$ is called its determining number, $Det(G)$. A graph $G$ is said to be $d$-distinguishable if there is a coloring of the vertices with $d$ colors so that only the trivial automorphism preserves the color classes. The smallest such $d$ is the distinguishing number, $Dist(G)$. If $Dist(G) = 2$, the cost of 2-distinguishing, $\rho(G)$, is the size of a smallest color class over all 2-distinguishing colorings of $G$. The Mycielskian, $\mu(G)$, of a graph $G$ is constructed by adding a shadow master vertex $w$, and for each vertex $v_i$ of $G$ adding a shadow vertex $u_i$ with edges so that the neighborhood of $u_i$ in $\mu(G)$ is the same as the neighborhood of $v_i$ in $G$ with the addition of $w$. That is, $N(u_i)=N_G(v_i)\cup\{w\}$. The generalized Mycielskian $\mu^{(t)}(G)$ of a graph $G$ is a Mycielskian graph with $t$ layers of shadow vertices, each with edges to layers above and below, and $w$ only adjacent to the top layer of shadow vertices. A graph is twin-free if it has no pair of vertices with the same set of neighbors. This paper examines the determining number and, when relevant, the cost of 2-distinguishing for Mycielskians and generalized Mycielskians of simple graphs with no isolated vertices. In particular, if $G \neq K_2$ is twin-free with no isolated vertices, then $Det(\mu^{(t)}(G)) = Det(G)$. Further, if $Det(G) = k \geq 2$ and $t \ge k-1$, then $Dist(\mu^{(t)}(G))=2$, and $Det(\mu^{(t)}(G)) = \rho(\mu^{(t)}(G))= k$. For $G$ with twins, we develop a framework using quotient graphs with respect to equivalence classes of twin vertices to give bounds on the determining number of Mycielskians. Moreover, we identify classes of graphs with twins for which $Det(\mu^{(t)}(G)) = (t{+}1) Det(G)$.

Introduction We have recently reported the crucial role of Galectin-3 (Gal3) in the progression of type 3 cardio-renal syndrome (CRS-3). Indeed, Gal3 overexpression after renal ischemia reperfusion (IRr) was associated with cardiac fibrosis and dysfunction, which were prevented by Gal3 pharmacological or genetic inhibition. Objective Our present aim was to better define the initial role of kidney Gal3 for triggering CRS-3. Method A murine irradiated and graft model having IRr was used to differentiate the Gal3 expressed by tissue (WT irradiated mice grafted with Gal3-/- bone marrow (BM) cells, WTGal3-/-BM) from Gal3 expressed by immune cells (Gal3-/- irradiated mice grafted with WT BM cells: Gal3-/-WTBM) and were killed after 2 or 28 days. Cardiac and renal phenotypes were evaluated using echocardiography and real-time PCR. Results After IRr, WTGal3-/-BM exhibit normal cardiac phenotype whereas Gal3-/-WTBM developed cardiac dysfunction and high Fibronectin (Fn) mRNA expression ( Fig. 1 A). In contrast, WTGal3-/-BM showed short- and long-term kidney damages with increased renal NGAL mRNA level by day 2 and increased Fn mRNA by 28d ( Fig. 1 B). In kidney after IRr, the increased levels of endothelial marker transcripts (ICAM-1, VCAM-1) mainly in WTGal3-/-BM mice suggested that tissue Gal3 expression is involved in the endothelial activation. Conclusion After IRr the organ dysfunction varies according to the Gal3 cell type origin; kidney Gal3 plays a major role in renal damage, whereas Gal3 from infiltrated BM cells in the heart is deleterious for cardiac function. It remains now to define how tissue Gal3 acts and interacts with endothelial cells, to assess Gal3 as a key-point for CRS-3 understanding.

Contemporary demographics reveal that the Asian Population is the fastest growing minority in the U.S. Thus, vocational rehabilitation counselors must be prepared to face cultural dynamics that can influence outcomes in the treatment process. While many people may view Asians as a homogenous population, people who are of Asian descent come from many places including, but not limited to Cambodia, China, India, Japan, Korea, Malaysia, Pakistan, the Philippine Islands, Thailand, Vietnam and Asian/Pacific Islander population. The present study provides information about the Asian culture relative to people with disabilities and seeks to give clinicians more tools to apply when working with people who are of Asian descent. Asians represent 4.8% of the civilian non-institutionalized population. Since the Asian/Pacific Islander population is a large racial ethnic group in the U.S., it is important to understand how vocational rehabilitation counselors educate them to live in their new land.The Asian population is one of the fastest-growing racial groups in the U.S. with the growth rate of Asians with disabilities steadily increasing. In the context of cultural differences, Asians with disabilities may avoid or refuse some services from rehabilitation agencies because negative family issues may not be shared beyond family members in a traditional aspect of Asians. Traditional Asian parents were educated that family is the central and primary unit and emphasize loyalty within the family (Committee of 100, 2001). Therefore, Asians consider a family member with a disability as a family problem. Because Asians believe that disability is shameful and represents family failure, such issues are hidden from the public and only handled within the families.Asians are defined as people who are originally from the Eastern Asia, Western Asia, Southeast Asia, or the Indian subcontinent. The most common countries represented are Cambodia, China, India, Japan, Korea, Malaysia, Pakistan, the Philippine Islands, Thailand, and Vietnam (U.S. Census Bureau, 2003). In this review, two groups of Asians are selected: Chinese (including people from mainland China, Taiwan, and Hong Kong) and South Korean.History of Asian Immigration in the United StatesDuring the 1800s, most of the Chinese living in the U.S. worked as merchants, domestics, farmers, and grocers in mainland China. The Chinese believed that the Gold Rush could bring them fortune; therefore, they came to the U.S., hoping to return home with wealth. Beginning in 1865, the businessman of Transcontinental Railroad project used the Gold Rush as an attraction to entice many Chinese to work in the railroad industry. The Chinese Exclusion Act of 1882 signed by President Chester A. Arthur prohibited all immigration of Chinese laborers; therefore, Chinese workers became part of an isolated community. As a result, the first generation Chinese immigrants built their own community by promoting small business ownerships in vocational sectors including restaurants, laundry, and merchandise retail (Le, 2009).In 1965, tire Immigration and Nationality Act opened the door for millions of Asians to immigrate (Le, 2009). Thus, Asians tended to reside in metropolitan areas in the U.S. Due to labor market discrimination, Asian Americans chose to be self-employed and often earned a higher salary than other ethnic groups. In terms of profitability, most Asian Americans hired their relatives as a cheap labor source and many of these relatives had to work very long hours. Because of the language barrier, the Asian family member often did not understand American laws and business regulations and were hired as cheap labor, usually working without benefits, insurance or knowledge of job safety (Le). This review of literature has been divided into the following five sections: (a) Asian demography and re- habilitation, (b) Traditional Chinese views of disabilities, (c) attitudes toward people with disabilities, (d) a South Korean view of disabilities, and (e) changing views of Asians toward individuals with disabilities. …

The relationship of receiving college and university training within the state vocational rehabilitation (VR) program to pre-VR consumer characteristics was investigated with a multiple direct logistic regression technique. A model containing 11 pre-VR characteristics predict the reception of college and university training for a multidisability set of consumers who received VR services ( R2 = .11). Characteristics represent both intrinsic and extrinsic properties of consumers associated with the outcome variable. A second analysis on the relationship between college and university training and competitive employment was conducted with a simple logistic regression technique. Consumers were less likely to secure employment following the reception of college and university training ( R2 = .00). Results are discussed in the context of plausible explanations and implications for career counseling.

The objective of this study was to identify VR services related to competitive employment for eligible consumers of the state VR program from two distinct groups: veterans who received college and university training and veterans who did not receive such training. A hierarchical logistical regression analysis was used on cases from the Rehabilitation Services Administration 911 database for fiscal year 2008 to test for such relationships. A total of 8 services were found related to employment for veterans who did not receive college training but only 2 services related to employment for veterans who received college training. Service needs of veterans differed based on their college training status. Implications of the findings and recommendations will be discussed for rehabilitation counseling professionals working with veterans with disabilities.

A recent glimpse into the employment trends of military veterans revealed patterns that differ from other groups. Consumers of the state vocational rehabilitation program who exited with an employment outcome as recorded on a Rehabilitation Services Administration database were investigated. A 2 X 5 chi-square analysis of veteran status and occupational category was conducted on 15,660 consumer cases, half of which represented military veterans. Military veterans with disabilities leaving the state vocational rehabilitation program during fiscal year 2008 were more proportionally represented in management, professional, natural resources, construction, maintenance, production, transportation, and material moving occupations and less represented in services as well as sales and office occupations. Rehabilitation practitioners are encouraged to use vocational assessment with military veterans and consider the results from a theoretical perspective.

Lacking sufficient evidence on the effectiveness of VR's college and university training service, this study sought to determine if college and university training was related to competitive employment for VR consumers with psychiatric disabilities. When controlling for gender, race and ethnicity, and level of education; validating the results with comparison data; and holding the analysis to stringent power considerations, the results indicated that VR consumers with psychiatric disabilities are more likely to become employed after receiving college and university training. Consumers with psychiatric disabilities were 33% more likely to become competitively employed following the reception of college and university training than other consumers with psychiatric disabilities who did not receive this service.

As more people with psychiatric disabilities seek postsecondary education opportunities to improve their employability and to eventually earn wages averaging higher than those without collegiate experience, institutions of higher education throughout the United States are seeing significant increases in the enrollments of this population. The State-Federal Vocational Rehabilitation (VR) Services program continues to serve as a valuable resource for people with disabilities who attend colleges and universities across the nation. A hierarchical logistic regression analysis was used to determine the effectiveness of VR services for people with psychiatric disabilities who also received college and university training. The Rehabilitation Services Administration 911 database for fiscal year 2006 was used to identify nine services related to the successful closure of this group of consumers. Results are discussed in relation to their importance for rehabilitation counselors.

The purpose of this study was to determine the predictive ability of vocational rehabilitation services for deaf and hard of hearing consumers who received college and university training. The RSA-911 database for fiscal year 2004 was analyzed to evaluate the effectiveness of 21 services in leading to competitive employment. A model predicting competitive employment included job search assistance, job placement, maintenance, rehabilitation technology, transportation, information and referral services, and other services. Results from the logistic regression analysis are discussed in relation to the implications to practitioners and educators.

A review of the literature revealed 20 studies that examined the extent to which cognitive behavioral therapy (CBT), supportive-expressive group therapy (SEGT), and a combination of these two treatments impact women with breast cancer. Based on this review, it is determined that CBT and SEGT have repeated experimental support for positively altering certain affective disturbances for this population. However, all three treatments were found to improve the lives of women with breast cancer. The combination of CBT and SEGT treatment approach did not have repeated positive results, as did the CBT and SEGT studies. The specific outcomes of these therapies are discussed along with the implications for researchers, therapists, and women with breast cancer.

A set of points W in Euclidean space is said to realize the finite group G if the isometry group of W is isomorphic to G. We show that every finite group G can be realized by a finite subset of some Rn, with n

It generally is held that the murine vagina develops from the urogenital sinus and the lower portion of the Mullerian ducts and that both endodermally derived sinus epithelium and mesodermally derived Mullerian epithelium contribute to the adult vagina. We tested Mullerian and urogenital sinus-derived vaginal epithelia for their ability to differentiate in response to various hormonal conditions and compared these responses to those of the in situ vagina. Tissue recombinants were prepared with 0-day Mullerian-derived vaginal epithelium and vaginal mesenchyme. Similarly, tissue recombinants containing urogenital sinus-derived vaginal epithelium were prepared with either 0-day sinus vaginal epithelium or 16-day fetal urogenital sinus epithelium and vaginal mesenchyme. Mullerian- or sinus-derived vaginal mesenchyme was used to construct the tissue recombinants; however, the source of the mesenchyme had no influence on the results. Tissue recombinants were grafted to the renal capsule of female mice, allowed to develop for 1 month, and exposed to various hormonal treatments. In diethylstilbestrol-treated hosts, all tissue recombinants regardless of the source of the epithelium were lined by a cornified epithelium. In contrast, only in tissue recombinants containing mesodermally derived Mullerian vaginal epithelium did the epithelium mucify in response to progesterone plus estrogen or become atrophic in ovariectomized hosts. These are the same epithelial modifications seen in the hosts' vagina. Tissue recombinants containing endodermally derived urogenital sinus epithelium or sinus vaginal epithelium and grafts of intact urogenital sinus maintained a stratified squamous noncornified epithelium in both ovariectomized and progesterone plus estrogen-treated hosts. Furthermore, in tissue recombinants containing Mullerian vaginal epithelium and vaginal mesenchyme, estrogen induced a slightly higher epithelial labeling index than in tissue recombinants containing urogenital sinus epithelium or sinus vaginal epithelium. The epithelial labeling index was the same regardless of the source of the vaginal mesenchyme. These results indicate that Mullerian-derived and sinus-derived vaginal epithelia are not equivalent and suggest that Mullerian vaginal epithelium displaces sinus vaginal epithelium during postnatal development. The replacement may result in part from a slight but consistently higher proliferation rate in Mullerian versus sinus vaginal epithelium. © 1996 Wiley-Liss, Inc.

A geometric graph G(bar) is a simple graph drawn in the plane, on points in general position, with straight-line edges. We call G(bar) a geometric realization of the underlying abstract graph G. A geometric homomorphism is a vertex map that preserves adjacencies and crossings (but not necessarily non-adjacencies or non-crossings). This work uses geometric homomorphisms to introduce a partial order on the set of isomorphism classes of geometric realizations of an abstract graph G. We say G(bar) precedes G(hat) if G(bar) and G(hat) are geometric realizations of G and there is a vertex-injective geometric homomorphism from G(bar) to G(hat). This paper develops tools to determine when two geometric realizations are comparable. Further, for 3 \leq n \leq 6, this paper provides the isomorphism classes of geometric realizations of P_n, C_n and K_n, as well as the Hasse diagrams of the geometric homomorphism posets of these graphs. The paper also provides the following results for general n: the poset of P_n and C_n has a unique minimal element and a unique maximal element; if k \leq n then the poset of P_k (resp., the poset of C_k) is a subposet of the poset for P_n (resp., C_n); and the poset for K_n contains a chain of length n-2., 42 pages, 25 figures; co-author added in replaced version

The epithelium of the mammalian vagina arises from two distinct germ layers, endoderm from the urogenital sinus and mesoderm from the Mullerian ducts. While neonatal vaginal epithelium can be induced to form prostate which is normally an endodermal derivative, it has not been determined whether this ability to form prostate is shared by both mesoderm- and endo-derm-derived vaginal epithelia. To test the competence of vaginal epithelia we have isolated sinus-derived and Miillerian-derived vaginal epithelia from newborn mice, combined them with rat urogenital sinus mesenchyme, and grown the tissue recombinants for 4 weeks in male athymic nude mice. Endoderm-derived sinus vaginal epithelium was induced to form prostatic tissue which expressed prostate-specific secretory proteins in 21 of 23 tissue recombinants. Mullerian-derived vaginal epithelium formed small ducts and cysts lined by a simple epithelium. These latter tissue recombinants lacked any evidence of prostatic secretory proteins. Similarly, endo-derm-derived urethral epithelium was induced to form prostate (17 of 17 cases), while mesoderm-derived uterine epithelium was not (0 of 13 cases). Therefore, the ability to form prostatic epithelium was limited to endodermal derivatives of the urogenital tract.

The cell surface proteoglycan, syndecan, exhibits molecular and histological dimorphism in the mouse uterus and vagina. In the mature vagina, syndecan is localized at the surfaces of the basal and intermediate cells of the stratified epithelium and has a modal molecular mass of ca. 92 kDa. The uterus expresses a larger form of syndecan (ca. 110 kDa) which is detected at the basolateral surfaces of the simple columnar epithelial cells. We have investigated whether epithelial-mesenchymal interactions influence the expression of syndecan in these organs by analyzing tissue recombinants composed of mouse epithelium and rat mesenchyme or vice versa with monoclonal antibody 281-2, which recognizes mouse syndecan. In tissue recombinants composed of newborn mouse uterine epithelium and rat vaginal stroma, the uterine epithelium was induced to form a stratified vaginal epithelium which expressed syndecan in same the pattern and mass typical of vaginal epithelium. Likewise, rat uterine stroma induced newborn mouse vaginal epithelium to undergo uterine development, and this epithelium exhibited a uterine pattern of syndecan expression. Although stromal cells normally express little syndecan in most adult organs, analysis of recombinants composed of mouse stroma and rat epithelium revealed that both uterine and vaginal mouse stromata synthesized syndecan that was larger (ca. 170–190 kDa) than the epithelial syndecans. A quantitative increase in the amount of stromal syndecan was evident when stroma was grown in association with epithelium in comparison to stroma grown by itself. These data suggest that epithelial-mesenchymal interactions influence the amount, localization, and mass of both epithelial and stromal syndecan.

Epithelium from the urogenital sinus-derived portion of the newborn mouse vagina when grown in association with uterine mesenchyme forms a “vaginal” stratified squamous non-cornified epithelium. However, the epithelium of these tissue recombinants composed of sinus vaginal epithelium plus uterine mesenchyme does not undergo the fluctuations in cytodifferentiation normally seen in vaginal epithelium during the estrous cycle (e.g., cornification and mucification). In this report we show that sinus vaginal epithelium in association with uterine mesenchyme proliferated in response to estradiol but failed to cornify in response to diethylstilbestrol (DES), even though both the epithelium and the stroma had estrogen receptors. However, if sinus vaginal epithelium that had been grown in combination with uterine mesenchyme was re-isolated from the tissue recombinant and recombined with fresh vaginal mesenchyme, the epithelium cornified in response to DES. These results indicate that the proliferative and the cytodifferentiation response to estrogen could be uncoupled and that sinus vaginal epithelium required vaginal stroma to cornify in response to DES.

The Navy utilizes matrices to analyze radar signals to determine the direction and velocity of aircraft. Matrix analysis is also useful in the sonar classification of submarines. One powerful tool for obtaining information about matrices is wedge theory. (The traditional terminology is compound matrix theory, whereas modern texts speak of mappings on the exterior algebra.) Wedge theory is a fundamental tool in multilinear algebra with important applications to group representations and tensor analysis. Current research indicates that it may also be useful in analyzing noisy data matrices, but this potential has not yet been fully explored. The purpose of this report is to collect details about wedge theory, in one accessible place, to facilitate future exploration of this topic. First, basic properties of the wedge operation are given along with definitions and examples. Then, an application to calculating the rank of a matrix with noise is considered. Finally, since the basic constructions can now be easily implemented on desktop computer algebra systems, the procedures for several such packages are illustrated.

It generally is held that the murine vagina develops from the urogenital sinus and the lower portion of the Müllerian ducts and that both endodermally derived sinus epithelium and mesodermally derived Müllerian epithelium contribute to the adult vagina. We tested Müllerian and urogenital sinus-derived vaginal epithelia for their ability to differentiate in response to various hormonal conditions and compared these responses to those of the in situ vagina. Tissue recombinants were prepared with 0-day Müllerian-derived vaginal epithelium and vaginal mesenchyme. Similarly, tissue recombinants containing urogenital sinus-derived vaginal epithelium were prepared with either 0-day sinus vaginal epithelium or 16-day fetal urogenital sinus epithelium and vaginal mesenchyme. Müllerian- or sinus-derived vaginal mesenchyme was used to construct the tissue recombinants; however, the source of the mesenchyme had no influence on the results. Tissue recombinants were grafted to the renal capsule of female mice, allowed to develop for 1 month, and exposed to various hormonal treatments. In diethylstilbestrol-treated hosts, all tissue recombinants regardless of the source of the epithelium were lined by a cornified epithelium. In contrast, only in tissue recombinants containing mesodermally derived Müllerian vaginal epithelium did the epithelium mucify in response to progesterone plus estrogen or become atrophic in ovariectomized hosts. These are the same epithelial modifications seen in the hosts' vagina. Tissue recombinants containing endodermally derived urogenital sinus epithelium or sinus vaginal epithelium and grafts of intact urogenital sinus maintained a stratified squamous noncornified epithelium in both ovariectomized and progesterone plus estrogen-treated hosts. Furthermore, in tissue recombinants containing Müllerian vaginal epithelium and vaginal mesenchyme, estrogen induced a slightly higher epithelial labeling index than in tissue recombinants containing urogenital sinus epithelium or sinus vaginal epithelium. The epithelial labeling index was the same regardless of the source of the vaginal mesenchyme. These results indicate that Müllerian-derived and sinus-derived vaginal epithelia are not equivalent and suggest that Müllerian vaginal epithelium displaces sinus vaginal epithelium during postnatal development. The replacement may result in part from a slight but consistently higher proliferation rate in Müllerian versus sinus vaginal epithelium.

Ductal tips approximately 300 microM in length from adult rat dorsal (DP), lateral type 1 (L1), and lateral type 2 (L2) prostates were combined with mesenchyme from the embryonic urogenital sinus (UGM), neonatal seminal vesicle (SVM), or neonatal bulbourethral gland (BUGM) and grafted underneath the renal capsule of syngeneic male hosts. Following 1 month of in vivo growth, all tissue recombinants formed large masses of prostatic ductal tissue, which represented massive growth of the original population of prostatic epithelial cells. Examination of secretory protein expression in these tissue recombinants indicated that each mesenchyme influenced secretory function in the adult prostatic epithelium in a characteristic way. SVM maintained expression of DP-1 and probasin in prostatic ducts of DP, L1, and L2, which normally express these proteins. BUGM induced expression of C3 in prostatic ducts of the DP, L1, and L2, which normally do not express C3. UGM induced the expression of DP-1, probasin, and C3 in prostatic ducts from all dorsal-lateral lobes. Mesenchymal induction of massive epithelial growth, new ductal branching morphogenesis, and change in prostatic lobe identity are indicative of the presence of stem cells in adult prostatic epithelium because high proliferative capacity, tissue regeneration, and pluripotency (change in functional differentiation) are hallmarks of stem cells.

Androgen-dependent male urogenital development occurs via mesenchymal-epithelial interactions in which mesenchyme induces epithelial morphogenesis, regulates epithelial proliferation, and evokes expression of tissue-specific secretory proteins. Mesenchymal-epithelial interactions continue to be important into adulthood. For example, mesenchyme of the urogenital sinus (UGM) and seminal vesicle (SVM) induce dramatic morphologic and functional changes in various adult epithelia. Since adult epithelial cells are unquestionably responsive to mesenchymes that can elicit expression of alternative morphologic and functional phenotypes, established carcinomas might also be influenced by their connective tissue environment. In this regard, Dunning prostatic tumor has been induced by UGM or SVM to differentiate into tall columnar secretory epithelial cells. This change in cytodifferentiation is associated with a reduction in growth rate and loss of tumorigenesis. The role of soluble growth factors in the mechanism of mesenchymal-epithelial interactions is discussed.